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4. Graphing Trigonometric Functions

Graphs of Tangent and Cotangent Functions

4. Graphing Trigonometric Functions

Graphs of Tangent and Cotangent Functions

Guided videos.

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Introduction to Tangent Graph

Introduction to Tangent Graph

Introduction to Cotangent Graph

Introduction to Cotangent Graph

Additional 6 creators.

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Graphing Tan and Cot

Graphing Tan and Cot

Mario's Math Tutoring

PreCalculus - Trigonometry (26 of 54) Graphing y=tan(theta)

PreCalculus - Trigonometry (26 of 54) Graphing y=tan(theta)

Michel van Biezen

Graphing y=tanx

Graphing y=tanx

Carolee Pederson

How to Sketch y = tan(x) Quickly & Accurately

How to Sketch y = tan(x) Quickly & Accurately

Graphing Tangent-(y=tan x)

Graphing Tangent-(y=tan x)

MooMooMath and Science

Tangent graph | Graphs of trig functions

Tangent graph | Graphs of trig functions

Trigonometry - Transformations of tan and cot

Trigonometry - Transformations of tan and cot

MySecretMathTutor

Graphing the Tangent Function with a New Period

Graphing the Tangent Function with a New Period

Graph a Tangent Transformation in the Form: y=atan(bx+c)+d

Graph a Tangent Transformation in the Form: y=atan(bx+c)+d

Showing 9 of 9 videos

Practice this topic

Multiple Choice

Below is a graph of the function $y=\tan\left(bx\right)$ . Determine the value of b.

Multiple Choice

Below is a graph of the function $y=\cot\left(bx+\frac{\pi}{2}\right)$ . Determine the value of b.

Textbook Question

Graph each function over a one-period interval.

y = 3 sec [(1/4)x]

Textbook Question

Graph each function over a one-period interval.

y = - (1/2) csc (x + π/2)

Textbook Question

Graph each function over a one-period interval. See Examples 1–3.

y = tan 4x

Textbook Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = (1/2)csc (2x - π/4)

Textbook Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sec(πx - 2π)

Textbook Question

Graph each function over a one-period interval.

y = csc (x - π/4)

Textbook Question

Graph each function over a one-period interval. See Examples 1–3.

y = 2 tan x

Textbook Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 1/3 tan (3x - π/3)

Textbook Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = cot (x/2 + 3π/4)

Textbook Question

Graph each function over a one-period interval.

y = sec (x + π/4)

Textbook Question

Graph each function over a one-period interval.

y = 2 tan (¼ x)

Textbook Question

Graph each function over a one-period interval.

y = csc((1/2)x - π/4)

Textbook Question

Graph each function over a one-period interval.

y = cot (3x)

Textbook Question

Graph each function over a one-period interval.

y = (1/2) csc (2x + π/2)

Textbook Question

Graph each function over a one-period interval.

y = -2 tan (¼ x)

Textbook Question

Identify the circular function that satisfies each description.

period is π; function is decreasing on the interval (0, π)

Textbook Question

Match each function in Column I with the appropriate description in Column II.

I

y = -4 sin(3x - 2)

II

A. amplitude = 2, period = π/2, phase shift = ¾

B. amplitude = 3, period = π, phase shift = 2

C. amplitude = 4, period = 2π/3, phase shift = ⅔

D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

Textbook Question

Graph each function over a one-period interval.

y = 2 + 3 sec (2x - π)

Textbook Question

Graph each function over a one-period interval.

y = ½ cot (4x)

Textbook Question

Graph each function over a one-period interval.

y = ½ sec x

Textbook Question

Graph each function over a one-period interval.

y = 1 - (1/2) csc (x - 3π/4)

Textbook Question

Graph each function over a two-period interval.

y = tan(2x - π)

Textbook Question

Determine an equation for each graph.

Textbook Question

Graph each function over a two-period interval.

y = cot (3x + π/4)

Textbook Question

Graph each function over a one-period interval.

y = -1 + csc x

Textbook Question

Determine an equation for each graph.

Textbook Question

Graph each function over a two-period interval.

y = 1 + tan x

Textbook Question

Determine an equation for each graph.

Textbook Question

Graph each function over a two-period interval.

y = 1 - cot x

Textbook Question

Decide whether each statement is true or false. If false, explain why.

The tangent and secant functions are undefined for the same values.

Textbook Question

Graph each function over a two-period interval.

y = -1 + 2 tan x

Textbook Question

Decide whether each statement is true or false. If false, explain why.

The graph of y = sec x in Figure 37 suggests that sec(-x) = sec x for all x in the domain of sec x.

Textbook Question

Graph each function over a two-period interval.

y= -1 + (1/2) cot (2x - 3π)

Textbook Question

Graph each function over a two-period interval.

y = 1 - 2 cot [2(x + π/2)]

Textbook Question

Consider the function g(x) = -2 csc (4x + π). What is the domain of g? What is its range?

Textbook Question

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)

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Textbook Question

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)

<IMAGE>

Textbook Question

A rotating beacon is located at point A, 4 m from a wall. The distance a is given by

a = 4 |sec 2πt|,

where t is time in seconds since the beacon started rotating. Find the value of a for each time t. Round to the nearest tenth if applicable.

<IMAGE>

t = 1.24

Textbook Question

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)

<IMAGE>

Textbook Question

Consider the following function from Example 5. Work these exercises in order.

y = -2 - cot (x - π/4)

Based on the answer in Exercise 58 and the fact that the cotangent function has period π, give the general form of the equations of the asymptotes of the graph of y = -2 - cot (x - π/4).

Let n represent any integer.

Textbook Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = tan 3x

Textbook Question

Consider the following function from Example 5. Work these exercises in order.

y = -2 - cot (x - π/4)

Use the fact that the period of this function is π to find the next positive x-intercept. Round to the nearest hundredth.

Textbook Question

Fill in the blank(s) to correctly complete each sentence.

The graph of y = 3 + 5 cos (x + π/5) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)

Textbook Question

Match each function with its graph in choices A - D.

y = sec (x - π/2)

Textbook Question

Match each function with its graph in choices A–F.

y = tan (x - π )

A. <IMAGE> B. <IMAGE> C. <IMAGE>

D. <IMAGE> E. <IMAGE> F. <IMAGE>

Textbook Question

In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or secant. Give the equation of the function for the graph that you obtain.

Textbook Question

In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or secant. Give the equation of the function for the graph that you obtain.

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 3 csc x

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 1/2 csc x/2

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec x

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = sec x/3

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −2 csc πx

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −1/2 sec πx

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = csc(x − π)

Textbook Question

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec(x + π)

Textbook Question

In Exercises 45–52, graph two periods of each function. y = sec(2x + π/2) − 1

Textbook Question

In Exercises 45–52, graph two periods of each function. y = csc|x|

Textbook Question

In Exercises 53–54, let f(x) = 2 sec x, g(x) = −2 tan x, and h(x) = 2x − π/2. Graph two periods of y = (f∘h)(x).

Showing 60 of 60 practice