Question 1

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

Accepted Answer

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

Question 2

Convert the angle to a decimal in degrees. Round the answer to two decimal places.
-$$21 ^ { \circ } 17 ^ { \prime } 34 ^ { \prime \prime }$$

Accepted Answer

A)  21.22° 
B)  21.29° 
C)  21.34° 
D)  21.37° 
A)  21.22° 
B)  21.29° 
C)  21.34° 
D)  21.37°

Question 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.
-$\mathrm { r } = 5$ inches, $\theta = 2$ radians, $\mathrm { A } =$ ?

Accepted Answer

A)  $25 \mathrm { in } ^ { 2 }$ 
B)  50 in 2 
C)  10 in 2 
D)  5 in $^ { 2 }$ 
A)  $25 \mathrm { in } ^ { 2 }$ 
B)  50 in 2 
C)  10 in 2 
D)  5 in $^ { 2 }$

Question 4

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( - 3 , - 1 )$
Find $\sec \theta$.

Accepted Answer

A)  $- \frac { \sqrt { 10 } } { 3 }$ 
B)  $- \frac { 3 \sqrt { 5 } } { 5 }$ 
C)  $\frac { \sqrt { 5 } } { 2 }$ 
D)  $- \sqrt { 5 }$ 
A)  $- \frac { \sqrt { 10 } } { 3 }$ 
B)  $- \frac { 3 \sqrt { 5 } } { 5 }$ 
C)  $\frac { \sqrt { 5 } } { 2 }$ 
D)  $- \sqrt { 5 }$

Question 5

Convert the angle to D° M' S'' form. Round the answer to the nearest second.
-$112.56 ^ { \circ }$

Accepted Answer

A)  $112 ^ { \circ } 34 ^ { \prime } 36 ^ { \prime \prime }$ 
B)  $112 ^ { \circ } 33 ^ { \prime } 56 ^ { \prime \prime }$ 
C)  $112 ^ { \circ } 33 ^ { \prime } 36 ^ { \prime \prime }$ 
D)  $112 ^ { \circ } 31 ^ { \prime } 56 ^ { \prime \prime }$ 
A)  $112 ^ { \circ } 34 ^ { \prime } 36 ^ { \prime \prime }$ 
B)  $112 ^ { \circ } 33 ^ { \prime } 56 ^ { \prime \prime }$ 
C)  $112 ^ { \circ } 33 ^ { \prime } 36 ^ { \prime \prime }$ 
D)  $112 ^ { \circ } 31 ^ { \prime } 56 ^ { \prime \prime }$

Question 6

Write the word or phrase that best completes each statement or answers the question.
-Salt Lake City, Utah, is due north of Flagstaff, Arizona. Find the distance between Salt Lake City (40°45' north
latitude) and Flagstaff (35°16' north latitude). Assume that the radius of the Earth is 3960 miles. Round to
nearest whole mile.

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Convert the angle in radians to degrees.
-$\frac { 11 \pi } { 12 }$

Accepted Answer

A)  $150 ^ { \circ }$ 
B)  $210 ^ { \circ }$ 
C)  $160 ^ { \circ }$ 
D)  $165 ^ { \circ }$ 
A)  $150 ^ { \circ }$ 
B)  $210 ^ { \circ }$ 
C)  $160 ^ { \circ }$ 
D)  $165 ^ { \circ }$

Question 8

Answer the question.
-Which one of the equations below matches the graph?

Accepted Answer

A)  $y = 2 \cos \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = 2 \cos ( 3 x )$ 
D)  $y = - 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
A)  $y = 2 \cos \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = 2 \cos ( 3 x )$ 
D)  $y = - 2 \sin \left( \frac { 1 } { 3 } x \right)$

Question 9

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places.
-$- 308 ^ { \circ }$

Accepted Answer

A)  $- 5.37$
В) $- 5.36$ 
C)  $- 5.38$ 
D)  $- 5.35$ 
A)  $- 5.37$
В) $- 5.36$ 
C)  $- 5.38$ 
D)  $- 5.35$

Question 10

Solve the problem.
-If friction is ignored, the time $t$ (in seconds) required for a block to slide down an inclined plane is given by the fc
$$t = \sqrt { \frac { 2 a } { g \sin \theta \cos \theta } }$$
where $a$ is the length (in feet) of the base and $g \approx 32$ feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base $\mathrm { a } = 14$ when $\theta = 30 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a second. mula

Accepted Answer

A)  0.4 sec 
B)  2.4 sec 
C)  1.4 sec 
D)  1.1 sec 
A)  0.4 sec 
B)  2.4 sec 
C)  1.4 sec 
D)  1.1 sec

Question 11

Find an equation for the graph.
-  A) $y = 3 \sin \left( \frac { 1 } { 2 } x \right)$

Accepted Answer

B)  $y = 2 \sin ( 3 x )$ 
C)  $y = 3 \sin ( 2 x )$ 
D)  $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = 2 \sin ( 3 x )$ 
C)  $y = 3 \sin ( 2 x )$ 
D)  $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$

Question 12

Find the exact value of the expression. Do not use a calculator.
-$$\cos \frac { \pi } { 3 } + \tan \frac { 5 \pi } { 3 }$$

Accepted Answer

A)  $\frac { 1 - 2 \sqrt { 3 } } { 2 }$ 
B)  $\frac { \sqrt { 3 } + 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } + 3 } { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } + 3 } { 6 }$ 
A)  $\frac { 1 - 2 \sqrt { 3 } } { 2 }$ 
B)  $\frac { \sqrt { 3 } + 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } + 3 } { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } + 3 } { 6 }$

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.
-$\mathrm { s } = 4.84 \text { meters, } \theta = 2.2 \text { radians, } \mathrm { r } =$ ?

Accepted Answer

A)  1.1 m 
B)  2.2 m 
C)  1.5 m 
D)  0.45 m 
A)  1.1 m 
B)  2.2 m 
C)  1.5 m 
D)  0.45 m

Question 14

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

Accepted Answer

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

Question 15

Solve the problem.
-If $\tan \theta = - 4.5$, find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$.

Accepted Answer

A)  $- 11.5$ 
B)  $- 13.5 + 3 \pi$ 
C)  $- 13.5$ 
D)  undefined 
A)  $- 11.5$ 
B)  $- 13.5 + 3 \pi$ 
C)  $- 13.5$ 
D)  undefined

Question 16

Solve the problem.
-If friction is ignored, the time $t$ (in seconds) required for a block to slide down an inclined plane is given by the fc
$$t = \sqrt { \frac { 2 a } { g \sin \theta \cos \theta } }$$
where $a$ is the length (in feet) of the base and $g \approx 32$ feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base $\mathrm { a } = 12$ when $\theta = 58 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a second. mula

Accepted Answer

A)  1.5 sec 
B)  1.4 sec 
C)  0.5 sec 
D)  1.6 sec 
A)  1.5 sec 
B)  1.4 sec 
C)  0.5 sec 
D)  1.6 sec

Question 17

Solve the problem.
-The following data represents the average monthly minimum temperature for a certain city in California. $\begin{array}{l|c}
\text { Month, } \mathrm{x} & \begin{array}{c}
\text { Average Monthly } \
\text { Minimum } \
\text { Temperature, }{ }^{\circ} \mathrm{F}
\end{array} \
\hline \text { January, } 1 & 49.6 \
\text { February, } 2 & 50.8 \
\text { March, } 3 & 55.6 \
\text { April, } 4 & 57.5 \
\text { May, } 5 & 60.7 \
\text { June, } 6 & 63.6 \
\text { July, } 7 & 65.9 \
\text { August, } 8 & 65.6 \
\text { September, } 9 & 64.4 \
\text { October, } 10 & 62.1 \
\text { November, } 11 & 54.2 \
\text { December, } 12 & 50.1
\end{array}$

Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ tl 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 18

Find the exact value of the expression if θ = 30°. Do not use a calculator.
-$f ( \theta ) = \cos \theta \quad$ Find $11 f ( \theta )$.

Accepted Answer

A)  $\frac { 11 \sqrt { 3 } } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  $\frac { 11 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
A)  $\frac { 11 \sqrt { 3 } } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  $\frac { 11 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$

Question 19

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

Accepted Answer

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

Question 20

Write the equation of a sine function that has the given characteristics.
-Amplitude: 5
Period: 3

Accepted Answer

A)  $y = 4 \sin ( 3 x )$ 
B)  $y = 5 \sin \left( \frac { 2 } { 3 } \pi x \right)$ 
C)  $y = 3 \sin \left( \frac { 1 } { 2 } \pi x \right)$ 
D)  $y = \sin ( 3 \pi x ) + 4$ 
A)  $y = 4 \sin ( 3 x )$ 
B)  $y = 5 \sin \left( \frac { 2 } { 3 } \pi x \right)$ 
C)  $y = 3 \sin \left( \frac { 1 } { 2 } \pi x \right)$ 
D)  $y = \sin ( 3 \pi x ) + 4$

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

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $21 ^ { \circ } 17 ^ { \prime } 34 ^ { \prime \prime }$

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. - $\mathrm { r } = 5$ inches, $\theta = 2$ radians, $\mathrm { A } =$ ?

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 3 , - 1 )$ Find $\sec \theta$ .

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $112.56 ^ { \circ }$

Convert the angle in radians to degrees. - $\frac { 11 \pi } { 12 }$

Answer the question. -Which one of the equations below matches the graph?

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $- 308 ^ { \circ }$

Find the exact value of the expression. Do not use a calculator. - $\cos \frac { \pi } { 3 } + \tan \frac { 5 \pi } { 3 }$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { s } = 4.84 \text { meters, } \theta = 2.2 \text { radians, } \mathrm { r } =$ ?

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

Solve the problem. -If $\tan \theta = - 4.5$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad$ Find $11 f ( \theta )$ .

Write the equation of a sine function that has the given characteristics. -Amplitude: 5 Period: 3

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

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Exam 5: Trigonometric Functions

Find the exact value. Do not use a calculator. - tan⁡2π\tan 2 \pitan2π

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - 21∘17′34′′21 ^ { \circ } 17 ^ { \prime } 34 ^ { \prime \prime }21∘17′34′′

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. - r=5\mathrm { r } = 5r=5 inches, θ=2\theta = 2θ=2 radians, A=\mathrm { A } =A= ?

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - (−3,−1)( - 3 , - 1 )(−3,−1) Find sec⁡θ\sec \thetasecθ .

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - 112.56∘112.56 ^ { \circ }112.56∘

Convert the angle in radians to degrees. - 11π12\frac { 11 \pi } { 12 }1211π​