Question 1

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

Accepted Answer

A)  $\theta = \frac { 1 } { 7 }$ radians 
B)  $\theta = 6$ radians 
C)  $\theta = \frac { 1 } { 6 }$ radians 
D)  $\theta = 21$ radians 
E)  $\theta = 54$ radians 
A)  $\theta = \frac { 1 } { 7 }$ radians 
B)  $\theta = 6$ radians 
C)  $\theta = \frac { 1 } { 6 }$ radians 
D)  $\theta = 21$ radians 
E)  $\theta = 54$ radians B

Question 2

Evaluate the trigonometric function using its period as an aid. $$\cos \frac { 9 \pi } { 4 }$$

Accepted Answer

A) $\cos \frac { 9 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$ 
B)  $\cos \frac { 9 \pi } { 4 } = - \sqrt { 2 }$ 
C)  $\cos \frac { 9 \pi } { 4 } = \sqrt { 2 }$ 
D)  $\cos \frac { 9 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$ 
E)  $\cos \frac { 9 \pi } { 4 } = \infty$ 
A) $\cos \frac { 9 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$ 
B)  $\cos \frac { 9 \pi } { 4 } = - \sqrt { 2 }$ 
C)  $\cos \frac { 9 \pi } { 4 } = \sqrt { 2 }$ 
D)  $\cos \frac { 9 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$ 
E)  $\cos \frac { 9 \pi } { 4 } = \infty$ D

Question 3

Determine the period and amplitude of $y = 3 \cos \left( \frac { x } { 7 } + \frac { \pi } { 4 } \right)$

Accepted Answer

A)  period: $\frac { 2 \pi } { 7 } ;$ amplitude: 3 
B)  period: $- \frac { 2 \pi } { 7 } ;$ amplitude: $- 3$ 
C)  period: $\frac { \pi } { 7 }$; amplitude: 3 
D)  period: $7 \pi$; amplitude: 6 
E)  period: $14 \pi$; amplitude: 3 
A)  period: $\frac { 2 \pi } { 7 } ;$ amplitude: 3 
B)  period: $- \frac { 2 \pi } { 7 } ;$ amplitude: $- 3$ 
C)  period: $\frac { \pi } { 7 }$; amplitude: 3 
D)  period: $7 \pi$; amplitude: 6 
E)  period: $14 \pi$; amplitude: 3 E

Question 4

Describe the behavior of the function as $x$ approaches $\frac { \pi ^ { + } } { 2 } .$ 
$f ( x ) = 2 \tan x$

Accepted Answer

A) 
$f \rightarrow + \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
B) 
$f \rightarrow 0$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
C) 
$f \rightarrow - \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
D) 
$f \rightarrow 1$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
E) 
$f \rightarrow - 1$ as $x \rightarrow \frac { \pi } { 2 } ^ { + }$ 
A) 
$f \rightarrow + \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
B) 
$f \rightarrow 0$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
C) 
$f \rightarrow - \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
D) 
$f \rightarrow 1$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
E) 
$f \rightarrow - 1$ as $x \rightarrow \frac { \pi } { 2 } ^ { + }$

Question 5

$\text { If } B = 39 ^ { \circ } \text { and } a =7 
\text {, determine the value of } c \text {. Round to two decimal places. }$

Accepted Answer

A)  9.01 
B)  11.12 
C)  8.64 
D)  4.41 
E)  5.67 
A)  9.01 
B)  11.12 
C)  8.64 
D)  4.41 
E)  5.67

Question 6

Find the value of given trigonometric function. Round your answer to four decimal places. 
$\cos ( - 1.7 )$

Accepted Answer

A)  $\cos ( - 1.7 ) \approx - 0.2288$ 
B)  $\cos ( - 1.7 ) \approx 0.1288$ 
C)  $\cos ( - 1.7 ) \approx 0.0712$ 
D)  $\cos ( - 1.7 ) \approx - 0.0288$ 
E)  $\cos ( - 1.7 ) \approx - 0.1288$ 
A)  $\cos ( - 1.7 ) \approx - 0.2288$ 
B)  $\cos ( - 1.7 ) \approx 0.1288$ 
C)  $\cos ( - 1.7 ) \approx 0.0712$ 
D)  $\cos ( - 1.7 ) \approx - 0.0288$ 
E)  $\cos ( - 1.7 ) \approx - 0.1288$

Question 7

For the simple harmonic motion described by the trigonometric function, find the frequency. 
$d = 9 \cos \frac { 6 \pi } { 5 } t$

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 6 \pi } { 5 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $\frac { 5 \pi } { 6 }$ 
E)  $\frac { 5 } { 6 }$ 
A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 6 \pi } { 5 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $\frac { 5 \pi } { 6 }$ 
E)  $\frac { 5 } { 6 }$

Question 8

Select the graph of the function. (Include two full periods.) $$y = - \sin \frac { 2 \pi x } { 3 }$$

Accepted Answer

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

Question 9

Evaluate the trigonometric function using its period as an aid. 
$\cos \frac { 17 \pi } { 4 }$

Accepted Answer

A)  $\cos \frac { 17 \pi } { 4 } = \sqrt { 2 }$ 
B)  $\cos \frac { 17 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$ 
C)  $\cos \frac { 17 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$ 
D)  $\cos \frac { 17 \pi } { 4 } = - \sqrt { 2 }$ 
E)  $\cos \frac { 17 \pi } { 4 } = \infty$ 
A)  $\cos \frac { 17 \pi } { 4 } = \sqrt { 2 }$ 
B)  $\cos \frac { 17 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$ 
C)  $\cos \frac { 17 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$ 
D)  $\cos \frac { 17 \pi } { 4 } = - \sqrt { 2 }$ 
E)  $\cos \frac { 17 \pi } { 4 } = \infty$

Question 10

Determine whether the function is even, odd, or neither. 
$f ( x ) = x \csc \frac { x } { 2 }$

Accepted Answer

A)  Odd 
B)  Neither 
C)  Even 
A)  Odd 
B)  Neither 
C)  Even

Question 11

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\sec 230 ^ { \circ }$

Accepted Answer

A)  $\sec 230 ^ { \circ } \approx - 0.0222$ 
B)  $\sec 230 ^ { \circ } \approx 0.9778$ 
C)  $\sec 230 ^ { \circ } \approx - 0.9778$ 
D)  $\sec 230 ^ { \circ } \approx - 1.5557$ 
E)  $\sec 230 ^ { \circ } \approx - 0.5557$ 
A)  $\sec 230 ^ { \circ } \approx - 0.0222$ 
B)  $\sec 230 ^ { \circ } \approx 0.9778$ 
C)  $\sec 230 ^ { \circ } \approx - 0.9778$ 
D)  $\sec 230 ^ { \circ } \approx - 1.5557$ 
E)  $\sec 230 ^ { \circ } \approx - 0.5557$

Question 12

Find the supplement of the following angle. $136 ^ { \circ }$

Accepted Answer

A)  Supplement: $45 ^ { \circ }$ 
B)  Supplement: $44 ^ { \circ }$ 
C)  Supplement: $136 ^ { \circ }$ 
D)  Supplement: $46 ^ { \circ }$ 
E)  Supplement: $224 ^ { \circ }$ 
A)  Supplement: $45 ^ { \circ }$ 
B)  Supplement: $44 ^ { \circ }$ 
C)  Supplement: $136 ^ { \circ }$ 
D)  Supplement: $46 ^ { \circ }$ 
E)  Supplement: $224 ^ { \circ }$

Question 13

Find the angle $\alpha$ between two nonvertical lines $L _ { 1 } \text { and } L _ { 2 }$ . The angle $\alpha$ satisfies the equation $\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right|$ where $m _ { 1 }$ and $m _ { 2 }$ are slopes of $L _ { 1 }$ and $L _ { 2 }$, respectively.
(Assume that $m _ { 1 } m _ { 2 } \neq - 1$.)
$\begin{array} { l } 
L _ { 1 } : 3 x - 2 y = 5 \
L _ { 2 } : x + y = 1
\end{array}$ 
Round your answer to one decimal place.

Accepted Answer

A)  $78.7 ^ { \circ }$ 
B)  $79.7 ^ { \circ }$ 
C)  $81.7 ^ { \circ }$ 
D)  $80.7 ^ { \circ }$ 
E)  $82.7 ^ { \circ }$ 
A)  $78.7 ^ { \circ }$ 
B)  $79.7 ^ { \circ }$ 
C)  $81.7 ^ { \circ }$ 
D)  $80.7 ^ { \circ }$ 
E)  $82.7 ^ { \circ }$

Question 14

State the period of the function. $$y = \frac { 1 } { 2 } \sec \frac { \pi x } { 3 }$$

Accepted Answer

A)  10 
B)  6 
C)  $\frac { \pi } { 3 }$ 
D)  $6 \pi$ 
E)  8 
A)  10 
B)  6 
C)  $\frac { \pi } { 3 }$ 
D)  $6 \pi$ 
E)  8

Question 15

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$\sin ( - 0.75 )$$

Accepted Answer

A)  $\sin ( - 0.75 ) \approx - 2.6816$ 
B)  $\sin ( - 0.75 ) \approx 2.6816$ 
C)  $\sin ( - 0.75 ) \approx - 0.6816$ 
D)  $\sin ( - 0.75 ) \approx 1.6816$ 
E)  $\sin ( - 0.75 ) \approx 0.6816$ 
A)  $\sin ( - 0.75 ) \approx - 2.6816$ 
B)  $\sin ( - 0.75 ) \approx 2.6816$ 
C)  $\sin ( - 0.75 ) \approx - 0.6816$ 
D)  $\sin ( - 0.75 ) \approx 1.6816$ 
E)  $\sin ( - 0.75 ) \approx 0.6816$

Question 16

Find an algebraic expression that is equivalent to the expression.. $$\cos ( \arcsin 2 x )$$

Accepted Answer

A)  $\sqrt { 4 x ^ { 2 } - 1 }$ 
B) $\frac { 1 } { \sqrt { 1 + 4 x ^ { 2 } } }$ 
C)  $\sqrt { 1 + 4 x ^ { 2 } }$ 
D)  $\sqrt { 1 - 4 x ^ { 2 } }$ 
E)  $\frac { 1 } { \sqrt { 1 - 4 x ^ { 2 } } }$ 
A)  $\sqrt { 4 x ^ { 2 } - 1 }$ 
B) $\frac { 1 } { \sqrt { 1 + 4 x ^ { 2 } } }$ 
C)  $\sqrt { 1 + 4 x ^ { 2 } }$ 
D)  $\sqrt { 1 - 4 x ^ { 2 } }$ 
E)  $\frac { 1 } { \sqrt { 1 - 4 x ^ { 2 } } }$

Question 17

The angle of elevation of the sun is $34 ^ { \circ }$ . Find the length, l, of a shadow cast by a tree that is 53 feet tall. Round answer to two decimal places.

Accepted Answer

A)  $l = 79.09$ feet 
B)  $l = 94.78$ feet 
C)  $l = 63.93$ feet 
D)  $l = 59.45$ feet 
E)  $l = 78.58$ feet 
A)  $l = 79.09$ feet 
B)  $l = 94.78$ feet 
C)  $l = 63.93$ feet 
D)  $l = 59.45$ feet 
E)  $l = 78.58$ feet

Question 18

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

Accepted Answer

A)  $\theta = 150$ radians 
B)  $\theta = \frac { 6 } { 25 }$ radians 
C)  $\theta = \frac { 6 } { 31 }$ radians 
D)  $\theta = \frac { 25 } { 6 }$ radians 
E)  $\theta = 31$ radians 
A)  $\theta = 150$ radians 
B)  $\theta = \frac { 6 } { 25 }$ radians 
C)  $\theta = \frac { 6 } { 31 }$ radians 
D)  $\theta = \frac { 25 } { 6 }$ radians 
E)  $\theta = 31$ radians

Question 19

Find the exact values of the three trignometric functions of the angle $\theta$ $( \sin \theta , \cos \theta , \tan \theta )$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the traingle.) 
  
$a=2$

Accepted Answer

A) $\sin \theta = \sqrt { 2 } , \tan \theta = 1 , \quad \sec \theta = \frac { \sqrt { 2 } } { 2 }$ 
B) $\sin \theta = 1 , \tan \theta = \sqrt { 2 } , \quad \sec \theta = \frac { \sqrt { 2 } } { 2 }$ 
C) $\sin \theta = \frac { \sqrt { 2 } } { 2 } , \tan \theta = \sqrt { 2 } , \sec \theta = 1$ 
D) $\sin \theta = \frac { \sqrt { 2 } } { 2 } , \tan \theta = 1 , \sec \theta = \sqrt { 2 }$ 
E) $\sin \theta = 1 , \tan \theta = \frac { \sqrt { 2 } } { 2 } , \sec \theta = \sqrt { 2 }$ 
A) $\sin \theta = \sqrt { 2 } , \tan \theta = 1 , \quad \sec \theta = \frac { \sqrt { 2 } } { 2 }$ 
B) $\sin \theta = 1 , \tan \theta = \sqrt { 2 } , \quad \sec \theta = \frac { \sqrt { 2 } } { 2 }$ 
C) $\sin \theta = \frac { \sqrt { 2 } } { 2 } , \tan \theta = \sqrt { 2 } , \sec \theta = 1$ 
D) $\sin \theta = \frac { \sqrt { 2 } } { 2 } , \tan \theta = 1 , \sec \theta = \sqrt { 2 }$ 
E) $\sin \theta = 1 , \tan \theta = \frac { \sqrt { 2 } } { 2 } , \sec \theta = \sqrt { 2 }$

Question 20

Describe the behavior of the function as $x$ approaches $\frac { \pi ^ { + } } { 2 }$ $f ( x ) = 2 \tan x$

Accepted Answer

A) 
$f \rightarrow - \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
B) 
$f \rightarrow + \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 } .$ 
C) 
$f \rightarrow 0$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
D) 
$f \rightarrow - 1$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
E) 
$f \rightarrow 1$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$. 
A) 
$f \rightarrow - \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
B) 
$f \rightarrow + \infty$ as $x \rightarrow \frac { \pi ^ { + } } { 2 } .$ 
C) 
$f \rightarrow 0$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
D) 
$f \rightarrow - 1$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$ 
E) 
$f \rightarrow 1$ as $x \rightarrow \frac { \pi ^ { + } } { 2 }$.

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

Evaluate the trigonometric function using its period as an aid. $\cos \frac { 9 \pi } { 4 }$

Determine the period and amplitude of $y = 3 \cos \left( \frac { x } { 7 } + \frac { \pi } { 4 } \right)$

Describe the behavior of the function as $x$ approaches $\frac { \pi ^ { + } } { 2 } .$ $f ( x ) = 2 \tan x$

$\text { If } B = 39 ^ { \circ } \text { and } a =7 \text {, determine the value of } c \text {. Round to two decimal places. }$ $\text { If } B = 39 ^ { \circ } \text { and } a =7 \text {, determine the value of } c \text {. Round to two decimal places. }$

Find the value of given trigonometric function. Round your answer to four decimal places. $\cos ( - 1.7 )$

For the simple harmonic motion described by the trigonometric function, find the frequency. $d = 9 \cos \frac { 6 \pi } { 5 } t$

Select the graph of the function. (Include two full periods.) $y = - \sin \frac { 2 \pi x } { 3 }$

Evaluate the trigonometric function using its period as an aid. $\cos \frac { 17 \pi } { 4 }$

Determine whether the function is even, odd, or neither. $f ( x ) = x \csc \frac { x } { 2 }$

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\sec 230 ^ { \circ }$

Find the supplement of the following angle. $136 ^ { \circ }$

State the period of the function. $y = \frac { 1 } { 2 } \sec \frac { \pi x } { 3 }$

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\sin ( - 0.75 )$

Find an algebraic expression that is equivalent to the expression.. $\cos ( \arcsin 2 x )$

The angle of elevation of the sun is $34 ^ { \circ }$ . Find the length, l, of a shadow cast by a tree that is 53 feet tall. Round answer to two decimal places.

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

Describe the behavior of the function as $x$ approaches $\frac { \pi ^ { + } } { 2 }$ $f ( x ) = 2 \tan x$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Topics in Analytic Geometry

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Exam 4: Trigonometry

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

Evaluate the trigonometric function using its period as an aid. cos⁡9π4\cos \frac { 9 \pi } { 4 }cos49π​

Determine the period and amplitude of y=3cos⁡(x7+π4)y = 3 \cos \left( \frac { x } { 7 } + \frac { \pi } { 4 } \right)y=3cos(7x​+4π​)

Describe the behavior of the function as xxx approaches π+2.\frac { \pi ^ { + } } { 2 } .2π+​. f(x)=2tan⁡xf ( x ) = 2 \tan xf(x)=2tanx

If B=39∘ and a=7, determine the value of c. Round to two decimal places. \text { If } B = 39 ^ { \circ } \text { and } a =7 \text {, determine the value of } c \text {. Round to two decimal places. } If B=39∘ and a=7, determine the value of c. Round to two decimal places.

Find the value of given trigonometric function. Round your answer to four decimal places. cos⁡(−1.7)\cos ( - 1.7 )cos(−1.7)

For the simple harmonic motion described by the trigonometric function, find the frequency. d=9cos⁡6π5td = 9 \cos \frac { 6 \pi } { 5 } td=9cos56π​t

Select the graph of the function. (Include two full periods.) y=−sin⁡2πx3y = - \sin \frac { 2 \pi x } { 3 }y=−sin32πx​

Evaluate the trigonometric function using its period as an aid. cos⁡17π4\cos \frac { 17 \pi } { 4 }cos417π​

Determine whether the function is even, odd, or neither. f(x)=xcsc⁡x2f ( x ) = x \csc \frac { x } { 2 }f(x)=xcsc2x​

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) sec⁡230∘\sec 230 ^ { \circ }sec230∘

Find the supplement of the following angle. 136∘136 ^ { \circ }136∘

State the period of the function. y=12sec⁡πx3y = \frac { 1 } { 2 } \sec \frac { \pi x } { 3 }y=21​sec3πx​

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) sin⁡(−0.75)\sin ( - 0.75 )sin(−0.75)

Find an algebraic expression that is equivalent to the expression.. cos⁡(arcsin⁡2x)\cos ( \arcsin 2 x )cos(arcsin2x)

The angle of elevation of the sun is 34∘34 ^ { \circ }34∘ . Find the length, l, of a shadow cast by a tree that is 53 feet tall. Round answer to two decimal places.

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

Find the exact values of the three trignometric functions of the angle θ\thetaθ (sin⁡θ,cos⁡θ,tan⁡θ)( \sin \theta , \cos \theta , \tan \theta )(sinθ,cosθ,tanθ) shown in the figure. (Use the Pythagorean Theorem to find the third side of the traingle.) a=2a=2a=2

Describe the behavior of the function as xxx approaches π+2\frac { \pi ^ { + } } { 2 }2π+​ f(x)=2tan⁡xf ( x ) = 2 \tan xf(x)=2tanx

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Evaluate the trigonometric function using its period as an aid. $\cos \frac { 9 \pi } { 4 }$

Determine the period and amplitude of $y = 3 \cos \left( \frac { x } { 7 } + \frac { \pi } { 4 } \right)$

Describe the behavior of the function as $x$ approaches $\frac { \pi ^ { + } } { 2 } .$ $f ( x ) = 2 \tan x$

$\text { If } B = 39 ^ { \circ } \text { and } a =7 \text {, determine the value of } c \text {. Round to two decimal places. }$ $\text { If } B = 39 ^ { \circ } \text { and } a =7 \text {, determine the value of } c \text {. Round to two decimal places. }$

Find the value of given trigonometric function. Round your answer to four decimal places. $\cos ( - 1.7 )$

For the simple harmonic motion described by the trigonometric function, find the frequency. $d = 9 \cos \frac { 6 \pi } { 5 } t$

Select the graph of the function. (Include two full periods.) $y = - \sin \frac { 2 \pi x } { 3 }$

Evaluate the trigonometric function using its period as an aid. $\cos \frac { 17 \pi } { 4 }$

Determine whether the function is even, odd, or neither. $f ( x ) = x \csc \frac { x } { 2 }$

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\sec 230 ^ { \circ }$

Find the supplement of the following angle. $136 ^ { \circ }$

State the period of the function. $y = \frac { 1 } { 2 } \sec \frac { \pi x } { 3 }$

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\sin ( - 0.75 )$

Find an algebraic expression that is equivalent to the expression.. $\cos ( \arcsin 2 x )$

The angle of elevation of the sun is $34 ^ { \circ }$ . Find the length, l, of a shadow cast by a tree that is 53 feet tall. Round answer to two decimal places.

Describe the behavior of the function as $x$ approaches $\frac { \pi ^ { + } } { 2 }$ $f ( x ) = 2 \tan x$