Graphs of Tangent and Cotangent Functions - Online Tutor, Practice Problems & Exam Prep

Using the key features of the given graph, draw the reciprocal function that corresponds to it and identify the equation of the resulting function.

Using the key features of the given graph, draw the reciprocal function that corresponds to it and identify the equation of the resulting function.

Sketch the graph of the following cosecant function using three periods.

y = 4 csc x

Sketch the graph of the following cosecant function using two periods.

y = (1/3)csc(x/3)

Sketch the graph of the following secant function using three periods.

y = 4 sec x

Sketch the graph of the following secant function using two periods.

y = sec(x/2)

Sketch the graph of the following cosecant function using two periods.

y = - 3 csc(2πx)

Sketch the graph of the following secant function using two periods.

y = - (1/3)sec(2πx)

Sketch the graph of the following cosecant function using two periods.

y = csc(- π + 2x)

Sketch the graph of the following secant function using two periods.

y = 4sec(2x - π)

Sketch the graph of the following secant function using two periods.

y = sec(4x + π/4) - 1

Sketch the graph of the following cosecant function using two periods.

y = 2 csc |2x|

Sketch the graph of y = (a ○ b)(x) if:

a(x) = 3 sec x

b(x) = 3x - π/2

Graph the following function. Consider only one period.

$y=\sec\left(x-\frac32\pi\right)$

Graph the following function. Consider only one period.

$y=4\sec\left(\frac12x\right)$

Graph the following function. Consider only one period.

$y=\csc\left(x-\frac{3\pi}{4}\right)$

Graph the following function. Consider only one period.

$y=\sec\left(x+\frac{3\pi}{2}\right)$

Graph the following function. Consider only one period.

$y=\frac14\csc\left(4x+\frac{\pi}{2}\right)$

Graph the following function. Consider only one period.

$y=5+4\sec\left(2x-\frac{\pi}{2}\right)$

Find the domain and range of the function given below.

g(x) = -6 csc (8x + π/2)

A rotating light is placed at the top of a pole of height 7 m. Use the equation d = 7|sec 2πt| to find the distance d when t = 2.46 seconds.

Graph the following function. Consider only one period.

$y=\frac14\sec x$

Graph the following function. Consider only one period.

$y=-3+\csc x$

Graph the following function. Consider only one period.

$y=\tan\left(x-\frac{\pi}{3}\right)$

Graph the following function. Consider only one period.

$y=\tan\left(2x\right)$

Graph the following function. Consider only one period.

$y=4\tan x$

Graph the following function. Consider only one period.

$y=\csc\left(\frac14x-\frac{\pi}{2}\right)$

Graph the following function. Consider only one period.

$y=2-\frac14\csc\left(x-\frac{\pi}{4}\right)$

Write an equation that represents the graph of the trigonometric function shown.

Write an equation that represents the graph of the trigonometric function shown.

Write an equation that represents the graph of the trigonometric function shown.

Graph the following function. Consider only one period.

$y=5\tan\left(\frac12x\right)$

Graph the following function. Consider only one period.

$y=\cot\left(6x\right)$

Graph the following function. Consider only one period.

$y=-4\tan\left(\frac12x\right)$

Graph the following function. Consider only one period.

$y=\frac14\cot\left(8x\right)$

Graph the following function. Consider two periods.

$y=\tan\left(4x-\pi\right)$

Graph the following function. Consider two periods.

$y=\cot\left(5x+\frac{\pi}{2}\right)$

Graph the following function. Consider two periods.

$y=4+\tan x$

Graph the following function. Consider two periods.

$y=5-\cot x$

Graph the following function. Consider two periods.

$y=-3+4\tan\left(x\right)$

Graph the following function. Consider two periods.

$y=-3+\frac14\cot\left(3x-2\pi\right)$

Graph the following function. Consider two periods.

$y=4-2\cot\left(4\left(x+\frac{\pi}{4}\right)\right)$

Write an equation that represents the graph shown. The equation should be in simplest form ($b>0$ and phase shift is not included).

Find the amplitude, period, vertical translation, and phase shift for the following trigonometric function.

y = tan 7x

Write an equation that represents the graph shown. The equation should be in simplest form ($b>0$ and phase shift is not included).

Write an equation that represents the graph shown. The equation should be in simplest form ($b>0$ and phase shift is not included).

Find the amplitude, period, vertical translation, and phase shift for the following trigonometric function.

y = cot (x/4 - 5π/8)

Write the function having the following properties.

Increasing on the interval (-π/2, π/2) and having a period equal to π.

Find the amplitude, period, and phase shift of the trigonometric function.

y = -14 sin (7x - 5)

Determine the amplitude, period, phase shift, and vertical translation of the given trigonometric function.

y = (1/2) csc (4x - π/12)

Determine the amplitude, period, phase shift, and vertical translation of the given trigonometric function.

y = 2 sec (πx/2 - 4π)

Write the general equation of the asymptotes of the graph of the function given below.

$y=-5-\cot (x-\frac{\pi }{6})$

Find the next positive x-intercept of the function given below given that the least positive x-intercept is (0.33, 0). Round your answer to the nearest hundredth

y = -5 - cot(x - π/6)

Find the amplitude, period, vertical translation, and phase shift for the following trigonometric function.

y = (1/5)tan (5x - π/5)