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# Cotangent secant and cosecant

Tangent, Cotangent, Secant, and Cosecant The Quotient Rule In our last lecture, among other things, we discussed the function 1 x, its domain and its derivative. We also showed how to use the Chain Rule to ﬁnd the domain and derivative of a function of the form k(x) = 1 g(x); where g(x) is some function with a derivative Reciprocal Trigonometric Functions, secant, cosecant and cotangent, reciprocal identities, Definition of Cos, Sin, Tan, Csc, Sec, Cot, How to use the reciprocal identities, examples and step by step solution Cosecant is the reciprocal of sine. Secant is the reciprocal of cosine. Cotangent is the reciprocal of tangent. When solving right triangles the three main identities are traditionally used. However, the reciprocal functions (secant, cosecant and cotangent) can be helpful in solving trig equations and simplifying trig identities Calculate the secant, cosecant, and cotangent functions using the sides of a triangle. Click Create Assignment to assign this modality to your LMS. We have a new and improved read on this topic. Click here to view We have moved all content. Now we have reviewed these three functions of trigonometric, let us see the other three functions of trigonometry of cotangent, secant, and cosecant. Cotangent. First of all, we have the function of cotangent, which is defined as the reciprocal of the inverse of the function of a tangent. In mathematics, we write it as cot θ = 1 / tan θ

Secant Cosecant Cotangent - Explanation & Examples. Secant, cosecant, and cotangent are trigonometric functions derived from the three elementary functions sine, cosine, and tangent. This article will explain secant, cosecant, and cotangent functions, calculate them, find their signs, and finally give several examples with explanations Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions,.

### Secant, Cosecant, Cotangent (solutions, examples, videos

1. g Ratios For 3 numbers there are 6 ratios that can be made. Sine, Cosine and Tangent name 3 of the ratios, and the three you mentioned allow us to name all 6 ratios. Avoiding division. Example: If we know that the angle of elevation to the top of a 12 meter tall building is 40^@ and we want to find the distance to the building, call it x we could.
2. Hi, Can someone please help me with the following question. I would like to know how to input the cosecant, secant and cotangent functions and graph them using the HP Prime Graphing Calculator. Is there a function, like there is for sin, cos and tan, for cosec, sec and cot or do I have to inpu..
4. the secant function In a right triangle, the secant of an angle is the length of the hypotenuse divided by the length of the adjacent side. In a formula, it is abbreviated to just 'sec'. The secant function is a trigonometric function, one of three reciprocal functions, the other two being the cosecant function and the cotangent function
5. Cosecant, Secant & Cotangent mc-TY-cosecseccot-2009-1 In this unit we explain what is meant by the three trigonometric ratios cosecant, secant and cotangent. We see how they can appear in trigonometric identities and in the solution of trigonometrical equations. Finally, we obtain graphs of the functions cosecθ, secθ and cot�
6. Secant, Cosecant, and Cotangent : Simplifying Trig Functions As we explore trig identities and their graphs further, it is important to emphasize how each of them relate to one another. When we look at any given right triangle, we know that sine = the opposite side (from a chosen angle) over the hypotenuse , which is the longest side

Worked example where we walk through finding the major trig ratiosPractice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/mat.. This video shows how to find inverse trig ratios on graphing calculators

### Cotangent, Secant and Cosecant - Softschools

Answer (1 of 3): Take a look at this picture: I wish I could find a cleaner image; this has lots of stuff on it that makes it more complicated than we need it. Look at the triangle OAE in the picture. It's a right triangle, with sides OA = 1, AE = \tan \theta, OE = \sec \theta, with the altitud.. A Level Maths revision tutorial video.For the full list of videos and more revision resources visit www.mathsgenie.co.uk Secant, cosecant and cotangent are three trigonometric functions. They are the reciprocals of cosine, sine, and tangent. As shown, their graphs have patterns that are repeated over and over along.

In addition to the three basic trig functions we've already looked at (Sine, Cosine, Tangent), there are three other related functions.These are Secant, Cosecant, and Cotangent. These functions have similar meanings as the first three, in that they represent the ratios of various side lengths of a right angle triangle, and can be used to find angles or unknown side lengths SECTION 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant 361 The Tangent Function The graph of the tangent function is shown below. As with the sine and cosine graphs, this graph tells us quite a bit about the function's properties Answer: 2 ������������������ question Four students wrote statements about cosecant, secant, and cotangent values as shown below. anik the cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1. isabella the cosecant - the answers to e-studyassistants.co

There might not be buttons for the secant, cosecant, and cotangent functions on the TI-84 Plus CE or any other TI-84 Plus graphing calculator, but that doesn.. Derivatives of Tangent, Cotangent, Secant, and Cosecant. We can get the derivatives of the other four trig functions by applying the quotient rule to sine and cosine. For instance, d d x ( tan. ⁡. ( x)) = ( sin. ⁡

Tangent, Cotangent, Secant, and Cosecant › See more all of the best online courses on www.dartmouth.edu Courses. Posted: (2 days ago) The range of cscx is the same as that of secx, for the same reasons (except that now we are dealing with the multiplicative inverse of sine of x, not cosine of x).Therefore the range of cscx is cscx ‚ 1 or cscx • ¡1: The period of cscx is the same as that. Graphing Cosecant Displaying all worksheets related to - Graphing Cosecant . Worksheets are Work graphs of sec and csc, Cosecant secant cotangent, Graphs of trig functions, Work properties of trigonometric functions, Graphs of other trigonometric functions, 13 trigonometricgraphswork, Precalculus work name secant and cosecant graphs 2, Graphing tangent functions work pdf Prezzi convenienti su Nd. Spedizione gratis (vedi condizioni After watching this video lesson, you will understand how the trigonometric functions cotangent, secant, and cosecant are related to the sine, cosine, and tangent functions. Updated: 02/14/202 Cosecant, secant, and cotangent are the reciprocals of sine, cosine, and tangent respectively, and are defined as: The values of the trigonometric functions can also be represented by the lengths of the line segments in a coordinate plane with a unit circle as show in the diagram below Sine, cosine, secant, and cosecant have period 2 π while tangent and cotangent have period π. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions. Ptolemy's identities, the sum and difference formulas for sine and cosine. Double angle formulas for sine and cosine The six trigonometric functions are called sine, cosine, tangent, cosecant, secant, and cotangent. Their domain consists of real numbers, but they only have practical purposes when these real numbers are angle measures. When a given angle, θ, is the input for a trigonometric function, like sine. The remaining trigonometric functions secant (), cosecant (), and cotangent are defined as the reciprocal functions of cosine, sine, and tangent, respectively. Rarely, these are called the secondary trigonometric functions Answer (1 of 4): For trigonometry, which has lots of applications outside of pure mathematics, it's enough to use sine, cosine, and tangent. In fact, for the first a thousand years of trigonometry, only one trig function was used; first it was the chord, later sines replaced chords. For calculus..

Secant, Cosecant, and Cotangent : Simplifying Trig Functions SOH - CAH - TOA is an extremely useful mnemonic to remember these relationships, and it is likely you have already been introduced to this simple reminder Answer (1 of 3): Mikayla Eckel Cifrese , thanks for the A2A. When you say we stopped using, what do you mean? I still use them.  There are modern uses for these trigonometric functions. versine, exsecant, etc.  have a direct relationship with the six commonly known functions, and so a.. Therefore secant is an even function. At this point, we advise you to ask your students to determine whether cosecant is even or odd with this same procedure as an exercise (note: it is an odd function, and the procedure is basically the same as the one above) Secant, Cosecant, and Cotangent : Simplifying Trig Functions SOH - CAH - TOA is an extremely useful mnemonic to remember these relationships, and it is likely you have already been introduced to this simple reminder. Read full answer Thanks (9) Do you have your own answer or clarification? Name Fiveable has free study resources like AP Calculus AB/BC Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions. Plus, join AP exam season live streams & Discord

Think about that for a second, that's positive, cosecant theta, that's also positive, 1 over positive and then cotangent is also positive. So normally there are six trig functions that we talk about, and we're going to list them in sort of table rows of free cosine, sine, tangent, secant, cosecant, cotangent. They're all positive Graph of Secant, Cosecant, and Cotangent. Here is a graph comparing sine and cosecant. The wave that is in red is y=sin (x), while the one in purple is y=csc (x). The relation between sine and cosecant is that cosecant is 1/sine. There reason why the graph of cosecant is not connected to each other is because there are times, where sin (x)=0. Using the alternate definition of sine and cosine as ratios of sides of right triangles, we can give alternate definitions of tangent, secant, cosecant, and cotangent. . . . . O scar H ad A H eap O f A pples is a mnemonic to remember that , , and . Starting with the known trigonometric identity we can derive two more identities by dividing both. Unit 4.5: Graphs of Tangent, Cotangent, Secant, and Cosecant. Tangent, cotangent, secant, and cosecant graphs are very different from the graphs of sine and cosine, and from the graphs of each other. A graph of tan (x) is shown below: Note that the graph of tan (x): Has frequent vertical asymptotes

Definition of sine, cosine, tangent, cotangent, secant, and cosecant. The lines of trigonometric functions. Trig Functions of Special Angles. Trig Tables of sines, cosines, tangents, cotangents, secants and cosecants. How to use the sine, cosine, tangent, and cotangent table. Examples. How to memorize the values of trigonometric function Trig Functions on Unit Circle. This dynamic diagram illustrates the three main trig functions -- sine, cosine and tangent -- along with their reciprocals -- cosecant, secant and cotangent. Note that the tangent and cotangent are actually lines tangent to the circle. The secant and cosecant cut through the curve, which is what secant lines do Notes & Guided Practice - Graphs of Cosecant and Secant 15 min. Teacher led introduction to new material. Then discuss the two example problems. Three Minute Drill 8 mins. Students have three minutes to silently complete as many problems as they can. Once they finish they have 30 seconds to check their work on the answer sheet Solution 12278: Calculating Secant, Cosecant, and Cotangent Trigonometric Functions on the TI-30X IIS/B. How do I calculate secant, cosecant, and cotangent trigonometric functions on the TI-30X IIS/B? TI scientific calculators do not feature the secant, cosecant, or cotangent trigonometric functions as separate keys. The properties of trigonometric functions must be used to calculate. Precalculus: Graphs of Tangent, Cotangent, Secant, and Cosecant Practice Problems 3. Solve the equation secx = 2 in the interval −π/2 ≤ x ≤ π/2. You should not need a calculator to solve this problem. Use what we know about secant to get started by converting into something with a cosine. secx = 1 cosx = 2 ⇒ cosx = 1 2 ### Secant, Cosecant, and Cotangent Functions ( Read

Test your knowledge of secant, cosecant and cotangent using this interactive quiz. Utilize the worksheet to identify study points to watch for.. Cosecant, Secant, and Cotangent Terrence Brenner, Juan Lacay, Hostos Community College Abstract: We demonstrate how a student could approach problems containing Cosecant, Secant, and Cotangent using only Sine, Cosine and Arctangent. Introduction Trigonometric functions are widely used in most branches of mathematics as well as i Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions. Derivatives of tan(x) and cot(x) This is the currently selected item. Derivatives of sec(x) and csc(x) Practice: Derivatives of tan(x), cot(x), sec(x), and csc(x) Next lesson. Optional videos. Video transcript

### Secant (sec), Cosecant (csc), and Cotangent (cot

• Details. The three less well-known functions in the family (cotangent, cosecant, secant) are the reciprocals of their better-known siblings: , , .The diagram clearly shows why cotangent becomes very large as the tangent gets smaller, and why sine and its reciprocal cosecant are both 1 when the red point reaches the top of the circle
• imum worth of 1; where the sine.
• Tangent and cotangent are cofunctions and complements. tan (π/2 - u) = cot (u) cot (π/2 - u) = tan (u) Secant and cosecant are cofunctions and complements. sec (π/2−u) = csc (u) csc (π/2−u) = sec (u) Given variable u as a real number or the radian measure of an angle, then the cofunction formulas in degrees are shown
• Solution 34752: Calculating Secant, Cosecant, and Cotangent Using the TI-83 Plus and TI-84 Plus Family of Graphing Calculators. How do I calculate secant, cosecant and cotangent on the TI-83 Plus and TI-84 Plus Family of graphing calculators? The TI-83 Plus and TI-84 Plus family of graphing calculators do not have built-in secant, cosecant and cotangent trigonometric functions. To compute.
• Start studying Tangent, Cotangent, Secant, and Cosecant. Learn vocabulary, terms, and more with flashcards, games, and other study tools  ### Secant Cosecant Cotangent - The Story of Mathematic

Section 7.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions. OBJECTIVE 1: Understanding the Graph of the Tangent Function and its Properties Recall that € y=tanx can equivalently be written € y = sin x cosx. Recall also that division by zero is never allowed. Therefore, the domain of � To find the x-intercepts and asymptotes of secant, cosecant, and cotangent, rewrite them in terms of sine and cosine. Notice that since secant and cosecant have 1 in the numerator and a trig function in the denominator, they can never equal zero; they do not have x-intercepts

### Trigonometric functions - Wikipedi

• Cosecant In triangle ABC, Cotangent In triangle ABC, Example 3: Find the secant, cosecant, and cotangent of angle B. Solution: First, we must find the length of the hypotenuse. We can do this using the Pythagorean Theorem: 2 2 2 2 2. 5 + 12 25 + 144 169 H =H =H =H = 13. Now we can find the secant, cosecant, and cotangent of angle B: 45
• SECTION 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant 399 ONGOING ASSESSMENT Self-Assessment: Ex. 5, 9, 29, 39 Embedded Assessment: Ex. 41, 42, 44, 59, 60 FIGURE 4.54 Characteristics of the cosecant function are inferred from the fact that it is the reciprocal of the sine function
• Chapter 4.5 - Graphs of Tangent, Cotangent, Secant, and Cosecant. Objectives: Analyze graphs of tangent, cotangent, secant and cosecant. Solve a trigonometric equation algebraically. Solve a trigonometric equation graphically. Solve applications
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C++ and Python Professional Handbooks : A platform for C++ and Python Engineers, where they can contribute their C++ and Python experience along with tips and tricks. Reward Category : Most Viewed Article and Most Liked Articl This calculator calculates sine, cosine, tangent, cotangent, secant, cosecant in degrees or radians. Notice We and selected partners use cookies or similar technologies as specified in the cookie policy. You can consent to the use of such technologies by closing this notice,. 4.5 Day 2 - Graphs of Secant & Cosecant. 87% average accuracy. 17 plays. 10th - 12th grade. Other. 5 months ago by. Share. Edit. Copy and Edit Start studying Tangent, Cotangent, Secant, and Cosecant Parent Graphs. Learn vocabulary, terms, and more with flashcards, games, and other study tools

### What is the purpose of the cotangent, secant, and cosecant

How is Cosecant (Hypotenuse Over Opposite), Secant (Hypotenuse Over Adjacent), Cotangent (Adjacent Over Opposite) abbreviated? CHOSHACAO stands for Cosecant (Hypotenuse Over Opposite), Secant (Hypotenuse Over Adjacent), Cotangent (Adjacent Over Opposite). CHOSHACAO is defined as Cosecant (Hypotenuse Over Opposite), Secant (Hypotenuse Over Adjacent), Cotangent (Adjacent Over Opposite) very rarely Answer: a. Clarification: Trigonometric ratios are only applicable to right-angled triangles whose angle is 90° between two sides of a triangle. 2. Trigonometric ratios are ______. a) sine, cosine and cotangent. b) sine, tangent, cotangent and secant. c) sine, cosine, tangent, cotangent, secant and cosecant. d) tangent, cotangent and secant ### Solved: The cosecant, secant and cotangent functions - HP

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• The secant, cotangent, and cosecant are all reciprocals of other functions. The secant is the reciprocal of the cosine function, the cotangent is the reciprocal of the tangent function, and the cosecant is the reciprocal of the sine function. The six trigonometric functions can be found from a point on the unit circle
• Cosecant, Secant and Cotangent. We can also divide the other way around (such as Adjacent/Opposite instead of Opposite/Adjacent): Cosecant Function
• Example Question #1 : Secant, Cosecant, Cotangent. If and , then which of the following must be true about . Possible Answers: Correct answer: Explanation: Since cosecant is negative, theta must be in quadrant III or IV. Since tangent is positive, it must be in quadrant I or III. Therefore, theta must be in quadrant III
• For certain values of x, the tangent, cotangent, secant and cosecant curves are not defined, and so there is a gap in the curve. [For more on this topic, go to Continuous and Discontinuous Functions in an earlier chapter.] Recall from Trigonometric Functions, that tan x is defined as: `tan x=(sin x)/(cos x)
• List of additional trigonometric functions include secant, cosecant, and cotangent. These functions are also established from the primary functions, like sine, cos and tan. It should be noted that the reciprocal of tan, cos, and sin are known as cotangent (cot), secant (sec), and cosecant (csc), respectively ### Trigonometric Functions - Cosecant, Secant, and Cotangent

Sine, cosine, secant, and cosecant have period 2 while tangent and cotangent have period . sin ( t + 2 ) = sin t. cos ( t + 2 ) = cos t. tan ( t + ) = tan t. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions. sin - t = -sin t Also, the period of secant and cosecant are the same as the period of cosine and sine, which is 2 π 2\pi 2 π. In trigonometric identities, we will see how to prove the periodicity of these functions using trigonometric identities. From the graphs of the tangent and cotangent functions, we see that the periods of secant and cosecant are both 2. Secant of an angle is the ratio of hypotenuse of the triangle to the base side of the angle. So, sec. θ = H y p o t e n u s e B a s e. Cotangent of an angle is the ratio of base side of angle to the perpendicular side to the angle. 45 ∘ = 1 2. As we know that cosecant is the reciprocal of sine. So, we get, cos Cosecant is the reciprocal of Sin, and thus Cosec x = 1/SinX. What is a Cosecant Function in Maths? There are different angle functions. Sine, cosine, cosecant, secant, tangent, and cotangent functions are the six elementary functions that are used and incorporated in trigonometry Parts of a Tangent and Cotangent Graph Visual Vertical Stretch/Compress: Secant and Cosecant graphs have a vertical stretch that would be equivalent to the amplitude of their reciprocal trig function. ������ ������������������ ������ ������ ������������������

### The Secant and Cosecant Functions - Trigonometr

• Deriving the Derivative Formulas for Tangent, Cotangent, Secant, Cosecant Many people memorize these formula but do not really understand where they come from. I show how you just use the derivative formulas for sine and cosine along with the quotient rule and chain rule to derive the rest
• Graphing Secant and Cosecant • Like the tangent and cotangent functions, amplitude does not play an important role for secant and cosecant functions. • Both have the same period of 2π, so we solve the phase shift and period with Bx + C = 0 & Bx + C = 2π • It is easier to graph y = A sec (Bx + C) or y = A csc (Bx + C) by graphing y = (1/A).
• Cosecant Secant Cotangent Displaying all worksheets related to - Cosecant Secant Cotangent . Worksheets are Cosecant secant cotangent, Graphs of tangent cotangent secant and cosecant, Work graphs of sec and csc, Tangent cotangent secant and cosecant, A aa aa f a g d b, 11 secant tangent and tangent tangent angles, Cosecant secant and cotangent, Maths module 8

### The Cosecant, Secant, and Cotangent Functions - YouTub

• Tangent, cotangent, secant, and cosecant are just various ratios of sine and cosine, and they're not quite as important. (Whenever I encounter those functions, the first thing I usually do is write them in terms of sine and cosine.
• Actually, the Pythagorean identity of cosecant and cot functions is proved mathematically in trigonometry by the geometrical method. So, let us study how to derive the proof of the Pythagorean identity for the co-secant and co-tangent functions. Write the relation between sides of the triangl
• Trigonometric Functions-Graphs. In this worksheet you will use the definition of the t- functions to plot the graphs of all six trigonometric functions. The first applet is for you to explore and observe how the graph of sine function is formed. In the other applet you will plot graph of cosine, tangent , secant and cosecant function as a point.
• Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions - Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions. The Graph of y = tan x 1. The domain is the set of all real numbers, except odd multiples of | PowerPoint PPT presentation | free to vie

### Secant, Cosecant, and Cotangent : Simplifying Trig Function

In article <32e94643...@nnrp.crl.com>, sad...@crl.com writes: > Why are there no built-ins for Secant, Cosecant, and Cotangent? Have you seen these functions built into any calculator? The HP48 allows you to create any functions you desire, to augment th The cofunction identities show the relationship between sine, cosine, tangent, cotangent, secant and cosecant. The value of a trigonometric function of an angle equals the value of the cofunction of the complement. Recall from geometry that a complement is defined as two angles whose sum is 90° Exercise Set 5.3: Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions Math 1330, Precalculus The University of Houston Chapter 5: Trigonometric Functions (d) State the domain and range of g() ()xx=cot . Do not base this answer simply on the limited domain from part (c), but the entire graph of g() ()xx=cot What is Cosecant equal to? The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x. The secant of x is 1 divided by the cosine of x: sec x = 1 cos x, and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x. = tan 5π 4. tan x = −∞ The invention discloses an anti-tangent, cotangent, secant and cosecant function demonstrating and graph drawing instrument which is made according to a rectangular coordinate definition of an anti-trigonometric function and by combining pushing-turning principles with slider-connecting rod characteristics. The instrument comprises a support, a demonstrating device, a drawing mechanism and a.

### Secant (sec), cosecant (csc) and cotangent (cot) example

Graph of Secant and Cosecant. Secant and cosecant are reciprocals of cosine and sine respectively, so their graphs should be related. Secant is graphed in Figure 6a and cosecant is in Figure 7a.Notice the graphs are identical except for a phase shift of π/2.Figure 6b graphs both secant and cosine on the same graph. Notice that x-intercepts on the cosine graph correspond to asymptotes on the. Sine, Cosine, Tangent, Cotangent, Secant and Cosecant. Sin A = Perpendicular/Hypotenuse Cos A = Base/Hypotenuse Tan A = Perpendicular/Base Sin, Cos and Tan are three. Start studying Cosecant and Secant Graphs. Learn vocabulary, terms, and more with flashcards, games, and other study tools

Graph the secant graph for 0 ≤ x ≤ 2π. Graph the cotangent graph for 0 ≤ x ≤ 2π. (don't need these pictures I have them) 3. Indicate whether each of the three reciprocal functions (cosecant, secant, and cotangent) is a periodic function. If so, state the period of each. 4. List the domain and range for the secant and cotangent functions Question: Explain why it is possible for tangent, cotangent, secant, and cosecant values to be greater than 1 even though it is not possible for cosine or sine values to be greater than 1. This problem has been solved! See the answer See the answer See the answer done loading For instance, Cosecant is the reciprocal of sine. Secant is the reciprocal of cosine. Cotangent is the reciprocal of tangent. When solving right triangles the three main identities are traditionally used. However, the reciprocal functions (secant, cosecant and cotangent) can be helpful in solving trig equations and simplifying trig identities Graphing Secant And Cosecant - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Graphing cosecant and secant, Work graphs of sec and csc, Graphs of tangent cotangent secant and cosecant, Cosecant secant cotangent, Academic pre calculus chapter 4, Writing graphs of csc and sec and tan and cot, Math analysis cp, Graphs of basic parent trigonometric. The graphs of the tangent, cotangent, secant, and cosecant functions all hav 00:53. Fill in the blank. sine, cosecant, tangent, and cotangent are _____ 01:49. Graphs of Trigonometric Functions Match the trigonometric function with one 02:37. Which of the following functions is even? \$-(a. Graphs of the Tangent, Cotangent, Cosecant and Secant Functions Section 5. 5 . Graphing the Tangent Function • Periodicity: Only need to graph on interval [0, p] Why? • Plot points and graph