1 Solve bx c = 2 and bx c = 2 to nd two consecutive vertical asymptotes. Graphing 1) Determine the x -values at the start and end of the period, set up and solve the following inequality for x. The range is (1 ;1). 2) Find the midpoints. 1) y = tan q 3 p 2 p3p 2 2p5p 2 3p7p 2 4p9p 2-6-5-4-3 Core TMM002 Outcome: Core skill demonstrated by students who successfully complete a Precalculus Course Standard: Functions: Demonstrate a deep understanding of functions whether they are described verbally, numerically, graphically, or algebraically (both explicitly and implicitly). $5.00. As with tangent and cotangent, the graph of secant has asymptotes. acyclovir cream price cvs; is h264 or h265 better for youtube; carbon county utah property records; raspberry pi ip67 case; what does 3 red hearts mean in texting from a guy Graph each function using radians. We can use what we know about the properties of the tangent function to quickly sketch a graph of any stretched and/or compressed tangent function of the form We focus on a single period of the function including the origin, because the periodic property enables us to extend the graph to the rest Since the sine is 0 at and at the multiples of, the cotangent is undefined at these points. Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies Inc,SMART Board Interactive Whiteboard The domain is Rn 2 +n. 3. -For tangent: 2 < < 2-For cotangent: 0< < (The endpoints are the asymptotes.) Tangent and Cotangent Functions - period, phase-shift, periodic functions, asymptotes, sine and cosine functions. + 24) y = 4tan (2q - 2p 3) - 2 5) y = 3cot (q 2 + p 4) - 26) y = 1 2 tan (q 3 - 5p 6) + 1. Lesson Summary The tangent function tan( )=sin() cos() is periodic with period . 2. Section 43 Graphs of the Tangent and Cotangent.notebook 3 Cotangent Function The cotangent is defined to be (cosx)/(sinx). (0, 1) Graphing Tangent Functions: The domain of y x= tan is the set of all real numbers except numbers of the form 2 ,+k where k is an integer. Angela Cala. can be obtained using the following steps (assuming !>0): Step 1: Calculate the period: # $. Homework. In fact, it is a horizontal flip and shift of the tangent function, as well see shortly in the next example. Period: The period of the graph is the horizontal Goal: To graph these trig functions Section 5.6: The graphs of Tangent, Cotangent, Secant, and Cosecant Thursday, January 30, 2014 12:44 PM Section 5.6 The graphs of Tangent, Cotangent, Secant, and Cosecant Page 1 Step 2: Find two neighboring vertical asymptotes. y = 3tan(x/2) 2. To sketch the full parent graph of cotangent, follow these steps: Find the vertical asymptotes so you can find the domain. 2. "c s o in s x x ". : =0 and = # $ Step 3: Find the x-intercept between the two asymptotes. Exercise 7 page 174: y f (x) tan4x. Graph Pattern: Use three dots per cycle which correspond to the three ticks between the vertical asymptotes. Use proper notation and descriptions in relation to the graphs of tangent and cotangent graph. Tangent: Think Low Medium High, positive slope, or always increasing Cotangent: Think High Medium Low, positive slope or always decreasing. The Graph of Tan(x) Well start with the table of values. It follows from the denitions of the trig A tangent graph is commonly described by 4 components. Exercise 7 page 174: y f (x) tan4x. Quiz : parent functions sec, csc, tan, cot Finish Worksheets cos(x) =0, that is , 2 5, 2 3, 2 x = Domain: 35, ,, 22 2 x Range: (, ) x-intercepts: when . First off, the amplitude is not an accurate factor for the tangent and cotangent functions because they both depart from the x-axis to infinity on both ends. Section 5.3b Graphs of the Tangent and Cotangent Functions 3 The Graph of Cotangent Recall: cos cot sin x x x so where cos 0x, cot x has an x- intercept and where sin 0x, cot x has an asymptote. Graphing Tangent and Cotangent Functions Graphs of = (!) Period: 4. : = # %$ and = # %$ For = (!) Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies Inc,SMART Board Interactive Whiteboard At each halfway point, the value of the function is This video goes over how to graph the tangent and the cotangent from the unit circle. Graph of the Tangent Function 2. Step 2: Find two neighboring vertical asymptotes. Identify transformations of these curves (horizontal/vertical shifts, amplitude, and period). y=2tanx 2 ! The cotangent function is the reciprocal of the tangent function. 10/26 4.6 Graphing Secant and Cosecant . This video goes over how to graph the tangent and the cotangent from the unit circle. Cosecant and se- and tangent. The graph of the cotangent func-tion is shown in Figure 4.62. 3. The process for graphing the other trigonometric functions is almost the same as sketching the graph of sine or cosine like in lesson 4-06. It will have zeros where the cosine function has zeros, and vertical asymptotes where the sine function has zeros. Range: (, +) 3. Readers ask: How Do You Graph A Tangent Graph?Find the vertical asymptotes so you can find the domain. These steps use x instead of theta because the graph is on the xy plane.Determine values for the range.Calculate the graphs x-intercepts.Figure out whats happening to the graph between the intercepts and the asymptotes. Recall also that division by zero is never allowed. Features of the Graph of Cotangent The cotangent graph has period Cotangent has domain k, where k is an integer Cotangent has range of all real numbers, ( , ) PDF. Tangent function: sin( ) ()nat cos( ) x You can take the graph of either of these basic functions and draw the graph of a more complicated function by making adjustments to the key elements of the basic function. The graph of y! In order to graph tangent and cotangent functions using transformations, begin with the parent table of values. Describe the graph of the function in terms of basic trigonometric functions. TMM 002 PRECALCULUS (Revised March 21, 2017) Recall also that division by zero is never allowed. The equations of the vertical asymptotes are x = +2 ,k where k is an integer. A tangent graph is commonly described by 4 components. The equations of the vertical asymptotes are x = +2 ,k where k is an integer. It will have zeros where the cosine function has zeros, and vertical asymptotes where the sine function has zeros.

This is because secant is defined as. The Graphs of Tangent, Cotangent, Cosecant, and Se-cant Were going to nd the graphs of these function using the same method we used for sin(x) and cos(x). Because cotangent is the quotient of cosine divided by sine, and. What are the key points of a tangent graph?The period of the tangent function is : The domain of the tangent function excludes 2+k 2 + k for all integers k ; The range of the tangent function is the set of all real numbers; 6.3 - Graphing the Tangent and Cotangent Trig Functions O sin x O cos x O f(x) = Tan x tan x (b Q\fA) Today's Objectives: 1 .ldentify the graphs of the tan and cot curves. View Graphing_tangent_and_cotangent_functions_practice.pdf from MATH 101 at Parsippany High. Thus, cot x! The tangent (BC) and cotangent (ED) functions are the lengths of the line segments tangent to the unit circle from the axis to the terminal ray of angle . Warm-up: Find the equation of the curve below.It shows the AC current from household outlet. Solve the equation cscx = 1 in the interval 2 x 5/2. First off, the amplitude is not an accurate factor for the tangent and cotangent functions because they both depart from the x-axis to infinity on both ends. Section 5.3b - Graphs of Tangent and Cotangent Functions . Cosecant and cotangent are odd functions, meaning that csc( ) = csc( ) and cot( ) = cot( ). Graphing Tangent, Cotangent, and Friends Name_____ Date_____ Block____ \ q2n0Y1f7` JKzuAtVa` GSBoMfWtrwFacrGeG aLYL\CM.j C pAHljl` qrIiSgAhxtRsK FrLeJszecrNv`evdn.-1-Graph each function using degrees. Section 43 Graphs of the Tangent and Cotangent.notebook 3 Cotangent Function The cotangent is defined to be (cosx)/(sinx). Read PDF Tangent And Secant Transformations Answer Key1 Graphing the Secant Graph with Multiple Transformations Learn to find the range of the secant function Graphs of Transformations of Tan, Sec, Cot, Csc Tangent \u0026 Cotangent Graphs w/ Transformations 6.5 Graphs of the Tangent, Cotangent, Secant and Cosecant Functions Page 8/35 It will look like the cosine function where the sine is essentially equal to 1, which is when xis near. Agenda: Section 5.3b Graphs of the Tangent and Cotangent Functions 3 The Graph of Cotangent Recall: cos cot sin x x x so where cos 0x, cot x has an x- intercept and where sin 0x, cot x has an asymptote. 10/27 4.6 Graphing Tangent and Cotangent. The tangent (BC) and cotangent (ED) functions are the lengths of the line segments tangent to the unit circle from the axis to the terminal ray of angle . Wednesday, September 10, 2014 2:03 PM Section 5.6 Graphs of tangent, cotangent, secant, and cosecant Page 1 Math 1316 Section 4.3 Class Notes 3 Examples: Graph each function over a one-period interval. + 24) y = 4tan (2q - 2p 3) - 2 5) y = 3cot (q 2 + p 4) - 26) y = 1 2 tan (q 3 - 5p 6) + 1. 4) Find the "Amplitude" points. The current lesson is devoted to examining graphs of the remaining trigonometric functions: the tangent,cotangent,secant,and cosecant. Graphing Tangent Transformations Graph each function using radians.

acyclovir cream price cvs; is h264 or h265 better for youtube; carbon county utah property records; raspberry pi ip67 case; what does 3 red hearts mean in texting from a guy Graphing tangent and cotangent functions Practice Worksheet Example: y = tan 4 x y = tan 4 x 8 period Precalculus: Graphs of Tangent, Cotangent, Secant, and Cosecant The Cotangent Function The tangent function is cotx= cosx sinx. Examples: 1) 2) ! is sometimes 0, the graph of the cotangent function may have asymptotes, just like with tangent. Notes page 1 and evens pages 2 to 5 Worksheets 2 to 5 odds Thursday . The secant (OC) and cosecant (OD) functions are the lengths on the rays (or secant lines), from the origin to its How to graph tangent and cotangent The biggest thing to remember here is that both these functions have as their default period instead of 2. Next page: Complete the table and graph 2 periods. Steps to Graph Tangent Use the following steps to sketch the graph of a tangent function of the form y = atan(bx c). The domain is Rn 2 +n. [Filename: triggraph.pdf] - Read File Online - Report Abuse. The Vertical Translation is equal to . Agenda:

: = # %$ and = # %$ For = (!) Graphs of the Tangent and Cotangent Functions . We can check that these identities are true by using that sine is an odd function and that cosine is even: Math 1316 Section 4.3 Class Notes 1 Graphs of the Tangent and Cotangent Functions Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/) Graphing & Writing Secant, Cosecant, Tangent and Cotangent Functions Date Topic Assignment Did It Fri 11/2 4.6 Graphing Secant and Cosecant NOTES p.1 & 2 Worksheet p. 3, 4 (#5 12) Mon 11/5 4.6 Graphing Tangent and Cotangent NOTES p. 5 Worksheet p. 6, 7 (#3 10) Tues 11/6 4.6 Graphing all 4: sec, csc, tan, cot For which values of are the identities in Exercise 12 valid? 5. There is only one transformation which is x u2192 2x. The domain is Rn 2 +n. The period is given by B S. Find two consecutive asymptotes by setting B x C equal to 0 and S and then solve for x. It is periodic with period . Then sketch the graph using radians. Title: Graphing tangent and cotangent functions practice (1).pdf Author: GVUser Created Date: 1/8/2016 9:08:47 AM Tangent function: sin( ) ()nat cos( ) x fx x x = =; Vertical asymptotes: when . Locate the vertical asymptotes and sketch two periods of the function. The cotangent function is the reciprocal of the tangent function. FOLLOW-UP Students will be able to generate the graphs for the tangent, cotangent, secant, Drawing the Graph To sketch a tangent and cotangent graph one needs to know how the constants A, B, and C of y = A tan (Bx + C) graph, affect the regular y = tan x and y = cot x graphs. 15. The graph of y = cot x will have asymptotes at the zeros of the sine function (Figure 4.51) and zeros at the zeros of the cosine function (Figure 4.52). Updated: 08/26/2021 Create an account 1 1 Cotangent Graph y = cot(x) The Cotangent Function f(x)=tanx - The graph is undefined A) y = 3 tan (x) EXAMPLE 1 Graphing a Tangent Function Describe the graph of the function y =-tan 2x in terms of a basic trigonometric y=2tanx 2 ! This video goes over how to graph the tangent and the cotangent from the unit circle. 1 Parts of a Tangent and Cotangent Graph Visual Vertical Stretch/Compress: Tangent and Cotangent do not have an amplitude because their range is all real numbers. However, they can be transformed by being vertically stretched or compressed. Section 7.7: Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions The tangent function, f(x) = tanxhas the following properties: 1. Be able to label "special" exact points on the graph of the tangent and cotangent function. Then sketch the graph using radians. Graph the Tangent and Cotangent Functions. Graphing Tangent and Cotangent Functions Graphs of = (!) The new x-values are found using _x+c, and the new y-values are found using ay+d. Section 7.7: Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions The tangent function, f(x) = tanxhas the following properties: 1. 4. Period: 4. 1 1 Cotangent Graph y = cot(x) The Cotangent Function f(x)=tanx - The graph is undefined Then sketch the graph using radians. Graphing tangent and cotangent functions Practice Worksheet Example: y = tan 4 x y = tan 4 x 8 period Notes - Graphing Tangent + Practice All Real Numbers Except x = Date: We will begin graphing our new tangent curves the same way we do when we encounter anything new.. .with a chart!! Be able to state a set of x coordinates that lead to a given y coordinates using sequences. This fun matching activity will help students practice identifying characteristics, graphs and notations functions of the; sine, cosine, tangent, cotangent, secant and cosecant. Section 7.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions. Cosecant and cotangent are odd functions, meaning that csc( ) = csc( ) and cot( ) = cot( ). Means: The angle whose tangent is 0.577 is 30 degrees. Is Arctangent the same as Cotangent? It turns out that arctan and cot are really separate things: cot (x) = 1/tan (x) , so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse. arctan (x) is the angle whose tangent is x. Graphing Tangent and Cotangent The graphs of or where , will have the following characteristics: 1. It is an odd function, so it is symmetric about the origin. Section 5.6: Graphs of Tangent, Cotangent,Secant, and Cosecant. Precalculus: Graphs of Tangent , Cotangent , Secant, and Cosecant The Cotangent Function The tangent function is cotx= cosx sinx. Domain : all real x x k + (k) 2 Properties of y = tan x period: To graph y = tan x, use the identity . . 2. Period: The period of the graph is the horizontal 1) y = tan 2 2) y = tan 2 3) y = tan ( + 5 4) 4) y = tan ( 4) 5) y = 1 + tan 6) y = tan + 2 7) y = tan ( 2) 2 8) y = 1 + tan ( 3 4) 9) y = 3tan 10) y = 1 2 tan 11) y = 1 2 2 +, for all integers . Graphs of cosecant, secant, and cotangent 274 0 0. Math 1316 Section 4.3 Class Notes 3 Examples: Graph each function over a one-period interval. Math 1316 Section 4.3 Class Notes 1 Graphs of the Tangent and Cotangent Functions Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/) It will have zeros where the cosine function has zeros, and vertical asymptotes where the sine function has zeros. OBJECTIVE 1: Understanding the Graph of the Tangent Function and its Properties Recall that y=tanx can equivalently be written y = sin x cosx. The current lesson is devoted to examining graphs of the remaining trigonometric functions: the tangent,cotangent,secant,and cosecant. Domain : all real x x k + (k) 2 Properties of y = tan x period: To graph y = tan x, use the identity . x y = tan (4x) Math 1316 Section 4.3 Class Notes 4 Exercise 13 page 174: y f (x) cot 3x. y = 3tan(x/2) 2. Thus, cot x = cos x sin x. pc_unit_10.4_n_key_v2.pdf: File Size: 2088 kb: File Type: pdf: Download File. Graphing Tangent, Cotangent, Secant, and Cosecant Graph each function using degrees. 3) c Vertical Shift: Draw a dotted horizontal line for the new middle. Using the sliders below the graph, you can change:The amount of energy in the wave by changing the amplitude, aThe frequency the wave by changing bThe phase shift of the wave by changing cThe vertical displacement of the wave by changing d cot x will have asymptotes at the zeros of the sine function (Figure 4.48) and zeros at the zeros of the cosine function (Figure 4.49). Range: (, +) 3.

For = (!) The range is (1 ;1). 5) Use the asymptotes as you draw the tangent graph. can be obtained using the following steps (assuming !>0): Step 1: Calculate the period: # $. It is an odd function, so it is symmetric about the origin.

Graphing Tangent and Cotangent Name_____ Period____ r _2n0J1J6E lKquBtEaQ WSDoLfctkwgaDr_eT bLDLBCa.I E gA[lhlN wrriwgvhgt_sJ UrCeYsAegrWvyeRd`. The Graph of Tan(x) Well start with the table of values.

How to graph y A Bx C cot( ): 1. Precalculus: Graphs of Tangent, Cotangent, Secant, and Cosecant The Cotangent Function The tangent function is cotx= cosx sinx. Unit 10.4 - Graphing Tangent & CoTangent Notes. Describe the graph of the function in terms of basic trigonometric functions. 3. acyclovir cream price cvs; is h264 or h265 better for youtube; carbon county utah property records; raspberry pi ip67 case; what does 3 red hearts mean in texting from a guy It will be a little more complicated than before, because these 2 The midpoint between these two vertical asymptotes will be an x-intercept. It flows downward to the right if #0 and upward to the right if #0. 5) Draw the basic shape of tangent or cotangent within the asymptotes. The tangent function has period . f(x) = Atan(Bx C) + D is a tangent with vertical and/or horizontal stretch/compression and shift. 3.Graph these curves by hand and on the calculator. 2. 1) y = tan 2 2) y = tan 2 3) y = tan ( + 5 4) 4) y = tan ( 4) 5) y = 1 + tan 6) y = tan + 2 7) y = tan ( 2) 2 8) y = 1 + tan ( 3 4) 9) y = 3tan 10) y = 1 2 tan 11) y = 1 2 In the previous lesson we constructed the graphs of the basic sine and cosine functions, and developed techniques for graphing more general waves related to these functions. 3. and = (!) Example: Graph the functions. + 24) y = 4tan (2q - 2p 3) - 2 5) y = 3cot (q 2 + p 4) - 26) y = 1 2 tan (q 3 - 5p 6) + 1. 4) Find the "Amplitude" points. 14. could argue that all of the above identities extend to any value of for which the tangent (and cotangent for the last two) is defined. The Phase Shift is equal to . The range of cotangent is ( , ), and the function is decreasing at each point in its range. OBJECTIVE 1: Understanding the Graph of the Tangent Function and its Properties Recall that y=tanx can equivalently be written y = sin x cosx. 5.5A Graphs of Tangent & Cotangent Objective: To graph the tranformations of the tangent and IV.Graph the cotangent function The values of cot(x) will be the reciprocal values of tan(x). Since the sine is 0 at and at the multiples of, the cotangent is undefined at these points. 6.3 - Graphing the Tangent and Cotangent Trig Functions O sin x O cos x O f(x) = Tan x tan x (b Q\fA) Today's Objectives: 1 .ldentify the graphs of the tan and cot curves. Identify transformations of these curves (horizontal/vertical shifts, amplitude, and period). 3) Take half a period more and less from the middle to draw the 32 asymptotes. 5.5A Graphs of Tangent & Cotangent Objective: To graph the tranformations of the tangent and IV.Graph the cotangent function The values of cot(x) will be the reciprocal values of tan(x). Students should be proficient working with the following families of The graph of y = cot x will have asymptotes at the zeros of the sine function (Figure 4.51) and zeros at the zeros of the cosine function (Figure 4.52). Graphing Tangent and Cotangent Functions The tangent function is not defined for all values of x, so its respective graph will have vertical asymptotes at Coo ) The Parent Gra h o Tan ent: Tangent Y = tan x Clio) GliD) cose X When / z- Domain: Range: The tangent function is Qd,, so it has Symmetry Periodic with a period of x-intercepts Graphing & Writing Secant, Cosecant, Tangent and Cotangent Functions Date Topic Assignment Did It Fri 11/2 4.6 Graphing Secant and Cosecant NOTES p.1 & 2 Worksheet p. 3, 4 (#5 12) Mon 11/5 4.6 Graphing Tangent and Cotangent NOTES p. 5 Worksheet p. 6, 7 (#3 10) Tues 11/6 4.6 Graphing all 4: sec, csc, tan, cot

Periods Cosecant, secant, and cotangent are periodic functions. Graph Pattern: Use three dots per cycle which correspond to the three ticks between the vertical asymptotes. It is periodic with period . Well use a table of values to plot some of the points, and then ll in the rest of the graph. Essentially you are just graphing a curve like y = x3 a bunch of times. If the graph will be reflected about the -axis. The new x-values are found using _x+c, and the new y-values are found using ay+d. GRAPHING 3 TRIGONOMETRIC FUNCTIONS 123 3.1 Basic Graphs 3.2 Graphing sin Bx and cos Bx 3.3 Graphing sin(Bx C) andcos(Bx C)3.4 Additional Applications 3.5 Graphing Combined Forms y k A y k A y k A y k A 3.6 Tangent, Cotangent, Secant, and Cosecant Functions Revisited Chapter 3 Group Activity: The graph is symmetric with respect to the origin, so the function is odd. Goal: To graph these trig functions Section 5.6: The graphs of Tangent, Cotangent, Secant, and Cosecant Thursday, January 30, 2014 12:44 PM Section 5.6 The graphs of Tangent, Cotangent, Secant, and Cosecant Page 1 7.6 Graphs of the Sine and Cosine Function Graph each function using degrees. Graphs of the Tangent and Cotangent Functions . 2) Find the midpoints. : =0 Find an x-intercept by taking the average of the two points on the x-axis where consecutive asymptotes pass. The range of cotangent is ( , ), and the function is decreasing at each point in its range. sin(x) =0 , that is .

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