Question 1

Draw the angle.
-$\frac { 7 \pi } { 4 }$

Accepted Answer

A) 
 
В)
  
C) 
  
D) 
  
A) 
 
В)
  
C) 
  
D)

Question 2

Without graphing the function, determine its amplitude or period as requested.
-$y = \frac { 3 } { 4 } \sin \left( - \frac { 4 \pi } { 5 } x \right) \quad$ Find the amplitude.

Accepted Answer

A)  $\frac { 3 } { 8 }$ 
B)  $\frac { 8 \pi } { 3 }$ 
C)  $\frac { 4 \pi } { 5 }$ 
D)  $\frac { 5 } { 2 }$ 
A)  $\frac { 3 } { 8 }$ 
B)  $\frac { 8 \pi } { 3 }$ 
C)  $\frac { 4 \pi } { 5 }$ 
D)  $\frac { 5 } { 2 }$

Question 3

Name the quadrant in which the angle θ lies.
-$\csc \theta > 0 , \quad \sec \theta > 0$

Accepted Answer

A)  I 
B)  II 
C)  III 
D)  IV 
A)  I 
B)  II 
C)  III 
D)  IV

Question 4

Graph the function. Show at least one period.
-$y=5 \sin (\pi x+4)$
 
 A)

Accepted Answer

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

Question 5

Find the exact value of the expression. Do not use a calculator.
-$$\tan \frac { \pi } { 6 } - \sin \frac { \pi } { 3 }$$

Accepted Answer

A)  $- \frac { \sqrt { 6 } } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 6 }$ 
C)  $\sqrt { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$ 
A)  $- \frac { \sqrt { 6 } } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 6 }$ 
C)  $\sqrt { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$

Question 6

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$$\theta = \frac { \pi } { 4 } \text { radians, } \mathrm { A } = 50 \text { square meters, } \mathrm { r } = \text { ? }$$

Accepted Answer

A)  11.29 m 
B)  4.43 m 
C)  19.63 m 
D)  78.5 m 
A)  11.29 m 
B)  4.43 m 
C)  19.63 m 
D)  78.5 m

Question 7

Solve the problem.
-The following data represents the normal monthly precipitation for a certain city in California. $\begin{array}{l|c}
\text { Month, x } & \begin{array}{c}
\text { Normal Monthly } \
\text { Precipitation, inches }
\end{array} \
\hline \text { January, 1 } & 6.06 \
\text { February, 2 } & 4.45 \
\text { March, 3 } & 4.38 \
\text { April, } 4 & 2.08 \
\text { May, 5 } & 1.27 \
\text { June, } 6 & 0.56 \
\text { July, } 7 & 0.17 \
\text { August, 8 } & 0.46 \
\text { September, } 9 & 0.91 \
\text { October, 10 } & 2.24 \
\text { November, 11 } & 5.21 \
\text { December, } 12 & 5.51
\end{array}$
Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ t] fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Accepted Answer

The answer of Solve the problem.
-The following data represents the...

Question 8

Find the exact value. Do not use a calculator.
-$\cos 2 \pi$

Accepted Answer

A)  1 
B)  $\frac { \sqrt { 2 } } { 2 }$ 
C)  0 
D)  undefined 
A)  1 
B)  $\frac { \sqrt { 2 } } { 2 }$ 
C)  0 
D)  undefined

Question 9

Match the given function to its graph.
-1) $y = 2 \sin ( 3 x )$
2) $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$
3) $y = - 2 \cos ( 3 x )$
4) $y = - 2 \cos \left( \frac { 1 } { 3 } x \right)$

Accepted Answer

A)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm {~B} , 4 \mathrm { D }$ 
B)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm { D } , 4 \mathrm {~B}$ 
C)  $1 \mathrm { D } , 2 \mathrm {~B} , 3 \mathrm {~A} , 4 \mathrm { C }$ 
D)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm { D } , 4 \mathrm {~B}$ 
A)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm {~B} , 4 \mathrm { D }$ 
B)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm { D } , 4 \mathrm {~B}$ 
C)  $1 \mathrm { D } , 2 \mathrm {~B} , 3 \mathrm {~A} , 4 \mathrm { C }$ 
D)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm { D } , 4 \mathrm {~B}$

Question 10

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\sec \frac { 19 \pi } { 4 }$

Accepted Answer

A)  $- \sqrt { 2 }$ 
B)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $- 2$ 
A)  $- \sqrt { 2 }$ 
B)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $- 2$

Question 11

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\sin \left( - 120 ^ { \circ } \right)$

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $\frac { - 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $\frac { - 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$

Question 12

Solve the problem.
-If $f ( \theta ) = \cos \theta$ and $f ( a ) = - \frac { 1 } { 12 }$, find the exact value of $f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )$

Accepted Answer

A)  $- 36$ 
B)  $- 12$ 
C)  $- \frac { 1 } { 12 }$ 
D)  $- \frac { 1 } { 4 }$ 
A)  $- 36$ 
B)  $- 12$ 
C)  $- \frac { 1 } { 12 }$ 
D)  $- \frac { 1 } { 4 }$

Question 13

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.
-$$\mathrm { r } = \frac { 1 } { 3 } \text { feet, } \mathrm { s } = 5 \text { feet, } \theta = \text { ? }$$

Accepted Answer

A)  $\frac { 5 } { 3 } \circ$ 
B)  15 radians 
C)  $15 ^ { \circ }$ 
D)  $\frac { 5 } { 3 }$ radians 
A)  $\frac { 5 } { 3 } \circ$ 
B)  15 radians 
C)  $15 ^ { \circ }$ 
D)  $\frac { 5 } { 3 }$ radians

Question 14

Solve the problem.
-A racetrack curve is banked so that the outside of the curve is slightly elevated or inclined above the inside of the curve. This inclination is called the elevation of the track. The maximum speed on the track in miles per
Hour is given by $\sqrt { \mathrm { r } ( 29000 + 41000 \tan \theta ) }$ where r is the radius of the track in miles and θ is the elevation in degrees. Find the maximum speed for a
Racetrack with an elevation of 26° and a radius of 0.6 miles. Round to the nearest mile per hour.

Accepted Answer

A)  37,953 mph 
B)  59,899 mph 
C)  193 mph 
D)  171 mph 
A)  37,953 mph 
B)  59,899 mph 
C)  193 mph 
D)  171 mph

Question 15

Graph the function.
-$y=-2 \csc \left(x-\frac{\pi}{4}\right)$

A)

Accepted Answer

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

Question 16

Solve the problem.
-The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The rest force $\mathrm { F }$, in Newtons, acting on a string pendulum is given by the formula
$$\mathrm { F } = \mathrm { mg } \sin \theta$$
where $\mathrm { m }$ is the mass in kilograms of the pendulum's bob, $g \approx 9.8$ meters per second per second is the acceleration due to gravity, and $\theta$ is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when $m = 0.8$ kilogram and $\theta = 60 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a Newton.

Accepted Answer

A)  $6.9 \mathrm {~N}$ 
B)  $6.8 \mathrm {~N}$ 
C)  $2.4 \mathrm {~N}$ 
D)  $3.9 \mathrm {~N}$ 
A)  $6.9 \mathrm {~N}$ 
B)  $6.8 \mathrm {~N}$ 
C)  $2.4 \mathrm {~N}$ 
D)  $3.9 \mathrm {~N}$

Question 17

Convert the angle in radians to degrees.
-$\frac { \pi } { 6 }$

Accepted Answer

A)  $1080 ^ { \circ }$ 
B)  $60 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $15 ^ { \circ }$ 
A)  $1080 ^ { \circ }$ 
B)  $60 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $15 ^ { \circ }$

Question 18

Solve the problem.
-For what numbers $\theta$ is $f ( \theta ) = \cot \theta$ not defined?

Accepted Answer

A)  integral multiples of $\pi \left( 180 ^ { \circ } \right)$ 
B)  all real numbers 
C)  odd multiples of $\pi \left( 180 ^ { \circ } \right)$ 
D)  odd multiples of $\frac { \pi } { 2 } \left( 90 ^ { \circ } \right)$ 
A)  integral multiples of $\pi \left( 180 ^ { \circ } \right)$ 
B)  all real numbers 
C)  odd multiples of $\pi \left( 180 ^ { \circ } \right)$ 
D)  odd multiples of $\frac { \pi } { 2 } \left( 90 ^ { \circ } \right)$

Question 19

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\sin ( - \pi )$

Accepted Answer

A)  0 
B)  $- 1$ 
C)  1 
D)  undefined 
A)  0 
B)  $- 1$ 
C)  1 
D)  undefined

Question 20

Find the exact value. Do not use a calculator.
-$\sec 30 ^ { \circ }$

Accepted Answer

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

Draw the angle. - $\frac { 7 \pi } { 4 }$

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 3 } { 4 } \sin \left( - \frac { 4 \pi } { 5 } x \right) \quad$ Find the amplitude.

Name the quadrant in which the angle θ lies. - $\csc \theta > 0 , \quad \sec \theta > 0$

Find the exact value of the expression. Do not use a calculator. - $\tan \frac { \pi } { 6 } - \sin \frac { \pi } { 3 }$

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = \frac { \pi } { 4 } \text { radians, } \mathrm { A } = 50 \text { square meters, } \mathrm { r } = \text { ? }$

Find the exact value. Do not use a calculator. - $\cos 2 \pi$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sec \frac { 19 \pi } { 4 }$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin \left( - 120 ^ { \circ } \right)$

Solve the problem. -If $f ( \theta ) = \cos \theta$ and $f ( a ) = - \frac { 1 } { 12 }$ , find the exact value of $f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = \frac { 1 } { 3 } \text { feet, } \mathrm { s } = 5 \text { feet, } \theta = \text { ? }$

Convert the angle in radians to degrees. - $\frac { \pi } { 6 }$

Solve the problem. -For what numbers $\theta$ is $f ( \theta ) = \cot \theta$ not defined?

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin ( - \pi )$

Find the exact value. Do not use a calculator. - $\sec 30 ^ { \circ }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 5: Trigonometric Functions

Draw the angle. - 7π4\frac { 7 \pi } { 4 }47π​

Without graphing the function, determine its amplitude or period as requested. - y=34sin⁡(−4π5x)y = \frac { 3 } { 4 } \sin \left( - \frac { 4 \pi } { 5 } x \right) \quady=43​sin(−54π​x) Find the amplitude.

Name the quadrant in which the angle θ lies. - csc⁡θ>0,sec⁡θ>0\csc \theta > 0 , \quad \sec \theta > 0cscθ>0,secθ>0

Graph the function. Show at least one period. - y=5sin⁡(πx+4)y=5 \sin (\pi x+4)y=5sin(πx+4) A) B) C) D)

Find the exact value of the expression. Do not use a calculator. - tan⁡π6−sin⁡π3\tan \frac { \pi } { 6 } - \sin \frac { \pi } { 3 }tan6π​−sin3π​

Find the exact value. Do not use a calculator. - cos⁡2π\cos 2 \picos2π

Match the given function to its graph. -1) y=2sin⁡(3x)y = 2 \sin ( 3 x )y=2sin(3x) 2) y=2sin⁡(13x)y = 2 \sin \left( \frac { 1 } { 3 } x \right)y=2sin(31​x) 3) y=−2cos⁡(3x)y = - 2 \cos ( 3 x )y=−2cos(3x) 4) y=−2cos⁡(13x)y = - 2 \cos \left( \frac { 1 } { 3 } x \right)y=−2cos(31​x)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - sec⁡19π4\sec \frac { 19 \pi } { 4 }sec419π​

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - sin⁡(−120∘)\sin \left( - 120 ^ { \circ } \right)sin(−120∘)

Solve the problem. -If f(θ)=cos⁡θf ( \theta ) = \cos \thetaf(θ)=cosθ and f(a)=−112f ( a ) = - \frac { 1 } { 12 }f(a)=−121​ , find the exact value of f(a)+f(a−2π)+f(a+4π)f ( a ) + f ( a - 2 \pi ) + f ( a + 4 \pi )f(a)+f(a−2π)+f(a+4π)

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - r=13 feet, s=5 feet, θ= ? \mathrm { r } = \frac { 1 } { 3 } \text { feet, } \mathrm { s } = 5 \text { feet, } \theta = \text { ? }r=31​ feet, s=5 feet, θ= ?

Graph the function. - y=−2csc⁡(x−π4)y=-2 \csc \left(x-\frac{\pi}{4}\right)y=−2csc(x−4π​) A) B) C) D)

Convert the angle in radians to degrees. - π6\frac { \pi } { 6 }6π​

Solve the problem. -For what numbers θ\thetaθ is f(θ)=cot⁡θf ( \theta ) = \cot \thetaf(θ)=cotθ not defined?

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - sin⁡(−π)\sin ( - \pi )sin(−π)

Find the exact value. Do not use a calculator. - sec⁡30∘\sec 30 ^ { \circ }sec30∘