Question 1

Graph the function.
-$y=4 \cos 6 x$

Accepted Answer

A)  $\frac { \pi } { 6 }$ 
B)  4 
C)  $2 \pi$ 
D)  $\frac { \pi } { 3 }$ 
A)  $\frac { \pi } { 6 }$ 
B)  4 
C)  $2 \pi$ 
D)  $\frac { \pi } { 3 }$

Question 2

Determine whether the given function is positive or negative for values of t in the specified quadrant.
-Quadrant IV, $\tan t$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 3

Evaluate without using a calculator by using ratios in a reference triangle.
-$\cot \frac { - 5 \pi } { 6 }$

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 3 }$ 
B)  $\sqrt { 3 }$ 
C)  $\frac { \sqrt { 3 } } { 3 }$ 
D)  $- \sqrt { 3 }$ 
A)  $- \frac { \sqrt { 3 } } { 3 }$ 
B)  $\sqrt { 3 }$ 
C)  $\frac { \sqrt { 3 } } { 3 }$ 
D)  $- \sqrt { 3 }$

Question 4

Find the specified quantity.
-Find the amplitude of $y = - 5 \cos \left( 2 x + \frac { \pi } { 4 } \right)$

Accepted Answer

A)  $\frac { \pi } { 2 }$ 
B)  5 
C)  $- 10$ 
D)  2 
A)  $\frac { \pi } { 2 }$ 
B)  5 
C)  $- 10$ 
D)  2

Question 5

Use a calculator to graph the function.
-$y=-\cos ^{2} x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Find approximate solutions for the equation in the interval $ -\pi<\mathbf{X}<\pi $. Round to three decimal places.
-$\tan x = 2 \csc x$

Accepted Answer

A)  $- 1.144,1.144$ 
B)  $- 1.571,1.571$ 
C)  $1.144$ 
D)  $- 0.785,0.785$ 
A)  $- 1.144,1.144$ 
B)  $- 1.571,1.571$ 
C)  $1.144$ 
D)  $- 0.785,0.785$

Question 7

Evaluate.
-$\tan ( 1,500,245 \pi ) - \tan ( 217,536 \pi )$

Accepted Answer

A)  $- 1$ 
B)  2 
C)  0 
D)  Undefined 
A)  $- 1$ 
B)  2 
C)  0 
D)  Undefined

Question 8

Determine whether the given function is positive or negative for values of t in the specified quadrant.
-Quadrant IV, csc $t$

Accepted Answer

A)  Negative 
B)  Positive 
A)  Negative 
B)  Positive

Question 9

Solve for x in the given interval.
-$$\tan x = - 1 , \frac { 3 \pi } { 2 } \leq x \leq 2 \pi$$

Accepted Answer

A)  $\frac { 5 \pi } { 3 }$ 
B)  $\frac { 7 \pi } { 4 }$ 
C)  $\frac { 5 \pi } { 4 }$ 
D)  $\frac { 11 \pi } { 6 }$ 
A)  $\frac { 5 \pi } { 3 }$ 
B)  $\frac { 7 \pi } { 4 }$ 
C)  $\frac { 5 \pi } { 4 }$ 
D)  $\frac { 11 \pi } { 6 }$

Question 10

Find the specified quantity.
-Find the period of $y = 2 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 2 } \right)$.

Accepted Answer

A)  $4 \pi$ 
B)  $2 \pi$ 
C)  $\frac { \pi } { 2 }$ 
D)  $8 \pi$ 
A)  $4 \pi$ 
B)  $2 \pi$ 
C)  $\frac { \pi } { 2 }$ 
D)  $8 \pi$

Question 11

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( - \sqrt { 3 } , - \sqrt { 7 } ) ;$ find $\csc \theta$

Accepted Answer

A)  $= \frac { \sqrt { 30 } } { 3 }$ 
B)  $\frac { \sqrt { 70 } } { 7 }$ 
C)  $- \frac { \sqrt { 70 } } { 10 }$ 
D)  $- \frac { \sqrt { 70 } } { 7 }$ 
A)  $= \frac { \sqrt { 30 } } { 3 }$ 
B)  $\frac { \sqrt { 70 } } { 7 }$ 
C)  $- \frac { \sqrt { 70 } } { 10 }$ 
D)  $- \frac { \sqrt { 70 } } { 7 }$

Question 12

Graph the function.
-$y=4 \cos x+\cos 3 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 13

Solve the equation.
-Solve $\sec \theta = \sqrt { 2 }$ for $\theta$, where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Accepted Answer

A)  $30 ^ { \circ }$ 
B)  $60 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $90 ^ { \circ }$ 
A)  $30 ^ { \circ }$ 
B)  $60 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $90 ^ { \circ }$

Question 14

On the given graph of $y = \cot x$, sketch the graph of $y = \cot ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Accepted Answer

The answer of  
On the given graph of \(y...

Question 15

Find the exact value of the real number y.
-$$y = \sin ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 3 }$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { 3 \pi } { 4 }$ 
A)  $\frac { \pi } { 3 }$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { 3 \pi } { 4 }$

Question 16

Find the exact value of the real number y.
-$$y = \arctan ( 1 )$$

Accepted Answer

A)  $\frac { \pi } { 4 }$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { \pi } { 3 }$ 
A)  $\frac { \pi } { 4 }$ 
B)  $\frac { 2 \pi } { 3 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { \pi } { 3 }$

Question 17

Find the exact solution to the equation without a calculator.
-$\tan \left( \tan ^ { - 1 } \mathrm { x } \right) = 20$

Accepted Answer

A)  10 
B)  20 
C)  0 
D)  40 
A)  10 
B)  20 
C)  0 
D)  40

Question 18

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary.
-$$f ( x ) = \sin 2 x - 3 \cos 2 x$$

Accepted Answer

A)  $\mathrm { a } = 1.41 , \mathrm {~b} = 2 , \mathrm {~h} = 0.62$ 
B)  $\mathrm { a } = 3.16 , \mathrm {~b} = 4 , \mathrm {~h} = 0.95$ 
C)  $a = 3.16 , b = 2 , h = 0.62$ 
D)  $a = 0.62 , b = 4 , h = 3.16$ 
A)  $\mathrm { a } = 1.41 , \mathrm {~b} = 2 , \mathrm {~h} = 0.62$ 
B)  $\mathrm { a } = 3.16 , \mathrm {~b} = 4 , \mathrm {~h} = 0.95$ 
C)  $a = 3.16 , b = 2 , h = 0.62$ 
D)  $a = 0.62 , b = 4 , h = 3.16$

Question 19

Graph the function.
-$y=-\csc 6 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$\sin ^ { - 1 } ( - 0.4848 )$

Accepted Answer

A)  $- 31 ^ { \circ }$ 
B)  $- 29 ^ { \circ }$ 
C)  $- 28 ^ { \circ }$ 
D)  $151 ^ { \circ }$ 
A)  $- 31 ^ { \circ }$ 
B)  $- 29 ^ { \circ }$ 
C)  $- 28 ^ { \circ }$ 
D)  $151 ^ { \circ }$

Graph the function. - $y=4 \cos 6 x$ $Graph the function. - y=4 \cos 6 x$

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant IV, $\tan t$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cot \frac { - 5 \pi } { 6 }$

Find the specified quantity. -Find the amplitude of $y = - 5 \cos \left( 2 x + \frac { \pi } { 4 } \right)$

Use a calculator to graph the function. - $y=-\cos ^{2} x$ $Use a calculator to graph the function. - y=-\cos ^{2} x$

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\tan x = 2 \csc x$

Evaluate. - $\tan ( 1,500,245 \pi ) - \tan ( 217,536 \pi )$

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant IV, csc $t$

Solve for x in the given interval. - $\tan x = - 1 , \frac { 3 \pi } { 2 } \leq x \leq 2 \pi$

Find the specified quantity. -Find the period of $y = 2 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 2 } \right)$ .

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( - \sqrt { 3 } , - \sqrt { 7 } ) ;$ find $\csc \theta$

Graph the function. - $y=4 \cos x+\cos 3 x$ $Graph the function. - y=4 \cos x+\cos 3 x$

Solve the equation. -Solve $\sec \theta = \sqrt { 2 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

$On the given graph of y = \cot x , sketch the graph of y = \cot ^ { - 1 } x as defined in the text. Give the domain and the range.$ On the given graph of $y = \cot x$ , sketch the graph of $y = \cot ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Find the exact value of the real number y. - $y = \sin ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$

Find the exact value of the real number y. - $y = \arctan ( 1 )$

Find the exact solution to the equation without a calculator. - $\tan \left( \tan ^ { - 1 } \mathrm { x } \right) = 20$

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = \sin 2 x - 3 \cos 2 x$

Graph the function. - $y=-\csc 6 x$ $Graph the function. - y=-\csc 6 x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\sin ^ { - 1 } ( - 0.4848 )$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 4: Trigonometric Functions

Graph the function. - y=4cos⁡6xy=4 \cos 6 xy=4cos6x

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant IV, tan⁡t\tan ttant

Evaluate without using a calculator by using ratios in a reference triangle. - cot⁡−5π6\cot \frac { - 5 \pi } { 6 }cot6−5π​

Find the specified quantity. -Find the amplitude of y=−5cos⁡(2x+π4)y = - 5 \cos \left( 2 x + \frac { \pi } { 4 } \right)y=−5cos(2x+4π​)

Use a calculator to graph the function. - y=−cos⁡2xy=-\cos ^{2} xy=−cos2x

Find approximate solutions for the equation in the interval −π<X<π -\pi<\mathbf{X}<\pi −π<X<π . Round to three decimal places. - tan⁡x=2csc⁡x\tan x = 2 \csc xtanx=2cscx

Evaluate. - tan⁡(1,500,245π)−tan⁡(217,536π)\tan ( 1,500,245 \pi ) - \tan ( 217,536 \pi )tan(1,500,245π)−tan(217,536π)

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant IV, csc ttt

Solve for x in the given interval. - tan⁡x=−1,3π2≤x≤2π\tan x = - 1 , \frac { 3 \pi } { 2 } \leq x \leq 2 \pitanx=−1,23π​≤x≤2π

Find the specified quantity. -Find the period of y=2sin⁡(14x−π2)y = 2 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 2 } \right)y=2sin(41​x−2π​) .

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - P(−3,−7);\mathrm { P } ( - \sqrt { 3 } , - \sqrt { 7 } ) ;P(−3​,−7​); find csc⁡θ\csc \thetacscθ

Graph the function. - y=4cos⁡x+cos⁡3xy=4 \cos x+\cos 3 xy=4cosx+cos3x

Solve the equation. -Solve sec⁡θ=2\sec \theta = \sqrt { 2 }secθ=2​ for θ\thetaθ , where 0∘≤θ≤90∘0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }0∘≤θ≤90∘

On the given graph of y=cot⁡xy = \cot xy=cotx , sketch the graph of y=cot⁡−1xy = \cot ^ { - 1 } xy=cot−1x as defined in the text. Give the domain and the range.

Find the exact value of the real number y. - y=sin⁡−1(22)y = \sin ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)y=sin−1(22​​)

Find the exact value of the real number y. - y=arctan⁡(1)y = \arctan ( 1 )y=arctan(1)

Find the exact solution to the equation without a calculator. - tan⁡(tan⁡−1x)=20\tan \left( \tan ^ { - 1 } \mathrm { x } \right) = 20tan(tan−1x)=20

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - f(x)=sin⁡2x−3cos⁡2xf ( x ) = \sin 2 x - 3 \cos 2 xf(x)=sin2x−3cos2x

Graph the function. - y=−csc⁡6xy=-\csc 6 xy=−csc6x

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - sin⁡−1(−0.4848)\sin ^ { - 1 } ( - 0.4848 )sin−1(−0.4848)

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Graph the function. - $y=4 \cos 6 x$ $Graph the function. - y=4 \cos 6 x$

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant IV, $\tan t$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cot \frac { - 5 \pi } { 6 }$

Find the specified quantity. -Find the amplitude of $y = - 5 \cos \left( 2 x + \frac { \pi } { 4 } \right)$

Use a calculator to graph the function. - $y=-\cos ^{2} x$ $Use a calculator to graph the function. - y=-\cos ^{2} x$

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\tan x = 2 \csc x$

Evaluate. - $\tan ( 1,500,245 \pi ) - \tan ( 217,536 \pi )$

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant IV, csc $t$

Solve for x in the given interval. - $\tan x = - 1 , \frac { 3 \pi } { 2 } \leq x \leq 2 \pi$

Find the specified quantity. -Find the period of $y = 2 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 2 } \right)$ .

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( - \sqrt { 3 } , - \sqrt { 7 } ) ;$ find $\csc \theta$

Graph the function. - $y=4 \cos x+\cos 3 x$ $Graph the function. - y=4 \cos x+\cos 3 x$

Solve the equation. -Solve $\sec \theta = \sqrt { 2 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

$On the given graph of y = \cot x , sketch the graph of y = \cot ^ { - 1 } x as defined in the text. Give the domain and the range.$ On the given graph of $y = \cot x$ , sketch the graph of $y = \cot ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Find the exact value of the real number y. - $y = \sin ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$

Find the exact value of the real number y. - $y = \arctan ( 1 )$

Find the exact solution to the equation without a calculator. - $\tan \left( \tan ^ { - 1 } \mathrm { x } \right) = 20$

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = \sin 2 x - 3 \cos 2 x$

Graph the function. - $y=-\csc 6 x$ $Graph the function. - y=-\csc 6 x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\sin ^ { - 1 } ( - 0.4848 )$