Question 1

Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\tan 45 ^ { \circ }$

Accepted Answer

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

Question 2

Solve the problem.
-On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 35 meters long and the shadow is 28 meters, how tall is the flag pole?

Accepted Answer

A) 21 m 
B) 49 m 
C) 45 m 
D) 63 m 
A) 21 m 
B) 49 m 
C) 45 m 
D) 63 m

Question 3

Find the exact value of the expression.
-cos (-390°)

Accepted Answer

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

Question 4

Find the exact value of the expression.
-csc 840°

Accepted Answer

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

Question 5

Evaluate.
-$$\sin ^ { 2 } 45 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ }$$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  2 
C)  0 
D)  1 
A)  $\frac { 1 } { 4 }$ 
B)  2 
C)  0 
D)  1

Question 6

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-cos ϴ = 0.49566425

Accepted Answer

A) 119.713561° 
B) 60.2864387° 
C) 299.713561° 
D) 29.7135613° 
A) 119.713561° 
B) 60.2864387° 
C) 299.713561° 
D) 29.7135613°

Question 7

Evaluate.
-$5 \sin ^ { 2 } 300 ^ { \circ } + \csc ^ { 2 } 150 ^ { \circ } - \sec ^ { 2 } 30 ^ { \circ }$

Accepted Answer

A)  $\frac { 29 } { 6 }$ 
B)  $\frac { 77 } { 12 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  $\frac { 13 } { 12 }$ 
A)  $\frac { 29 } { 6 }$ 
B)  $\frac { 77 } { 12 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  $\frac { 13 } { 12 }$

Question 8

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-csc 35°

Accepted Answer

A) sin 55° 
B) csc 145° 
C) sec 35° 
D) sec 55° 
A) sin 55° 
B) csc 145° 
C) sec 35° 
D) sec 55°

Question 9

Solve the problem.
-From the top of a vertical tower, 319 feet above the the surface of the earth, the angle of depression to a doghouse is 23° 3´. How far is it from the doghouse to the foot of the tower? Round your
Answer to the hundredths place when necessary.

Accepted Answer

A) 749.7 ft 
B) 852.3 ft 
C) 734.11 ft 
D) 762.1 ft 
A) 749.7 ft 
B) 852.3 ft 
C) 734.11 ft 
D) 762.1 ft

Question 10

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find $\sin \mathrm { A }$ when $\mathrm { b } = 33$ and $c = 55$

Accepted Answer

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

Question 11

Determine whether the statement is true or false.
-sin 60° = 2 sin 30°

Accepted Answer

A) True 
 B)False

Question 12

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-

$\mathrm { A } = 41.3 ^ { \circ } , \mathrm { b } = 2.5 \mathrm {~m}$
Round side lengths to one decimal place.

Accepted Answer

A)  $\mathrm { B } = 48.7 ^ { \circ } ; \mathrm { a } = 1.1 \mathrm {~m} ; \mathrm { c } = 4.0 \mathrm {~m}$ 
B)  $B = 48.7 ^ { \circ } ; a = 4.0 \mathrm {~m} ; \mathrm { c } = 4.7 \mathrm {~m}$ 
C)  $B = 48.7 ^ { \circ } ; a = 2.2 \mathrm {~m} ; \mathrm { c } = 3.3 \mathrm {~m}$ 
D)  $B = 48.7 ^ { \circ } ; a = 1.1 \mathrm {~m} ; \mathrm { c } = 2.7 \mathrm {~m}$ 
A)  $\mathrm { B } = 48.7 ^ { \circ } ; \mathrm { a } = 1.1 \mathrm {~m} ; \mathrm { c } = 4.0 \mathrm {~m}$ 
B)  $B = 48.7 ^ { \circ } ; a = 4.0 \mathrm {~m} ; \mathrm { c } = 4.7 \mathrm {~m}$ 
C)  $B = 48.7 ^ { \circ } ; a = 2.2 \mathrm {~m} ; \mathrm { c } = 3.3 \mathrm {~m}$ 
D)  $B = 48.7 ^ { \circ } ; a = 1.1 \mathrm {~m} ; \mathrm { c } = 2.7 \mathrm {~m}$

Question 13

Find the sign of the following.
-$\sin \frac { \theta } { 2 }$, given that $\theta$ is in the interval $\left( 180 ^ { \circ } , 270 ^ { \circ } \right)$.

Accepted Answer

A)  positive 
B)  negative 
A)  positive 
B)  negative

Question 14

Solve the problem.
-Find the exact value of x in the figure.

Accepted Answer

A)  $20 \sqrt { 5 }$ 
B)  $20 \sqrt { 2 }$ 
C)  $20 \sqrt { 6 }$ 
D)  $20 \sqrt { 3 }$ 
A)  $20 \sqrt { 5 }$ 
B)  $20 \sqrt { 2 }$ 
C)  $20 \sqrt { 6 }$ 
D)  $20 \sqrt { 3 }$

Question 15

Find the exact value of the expression.
-sin 30°

Accepted Answer

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

Question 16

Find the exact value of the expression.
-cot 60°

Accepted Answer

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

Question 17

Solve the problem.
-A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 14.1 miles due south of A, is N 32°57'W. How far is the fire from B (to the nearest tenth of a mile)?

Accepted Answer

A) 18.8 mi 
B) 19.8 mi 
C) 16.8 mi 
D) 17.8 mi 
A) 18.8 mi 
B) 19.8 mi 
C) 16.8 mi 
D) 17.8 mi

Question 18

Find all values of , if is in the interval [0, 360°) and has the given function value.
-$$\sin \theta = \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

A)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
C)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
D)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
C)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
D)  $150 ^ { \circ }$ and $210 ^ { \circ }$

Question 19

Solve the problem.
-A contractor needs to know the height of a building to estimate the cost of a job. From a point 90 feet away from the base of the building, the angle of elevation to the top of the building is found
To be 42° 17´. Find the height of the building. Round your answer to the hundredths place when
Necessary.

Accepted Answer

A) 84.75 ft 
B) 80.32 ft 
C) 81.85 ft 
D) 86.08 ft 
A) 84.75 ft 
B) 80.32 ft 
C) 81.85 ft 
D) 86.08 ft

Question 20

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\frac { 1 } { \tan 38 ^ { \circ } 46 ^ { \prime } }$

Accepted Answer

A)  $1.245232$ 
B)  $0.8030632$ 
C)  $1.2589754$ 
D)  $0.7942967$ 
A)  $1.245232$ 
B)  $0.8030632$ 
C)  $1.2589754$ 
D)  $0.7942967$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\tan 45 ^ { \circ }$

Solve the problem. -On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 35 meters long and the shadow is 28 meters, how tall is the flag pole?

Find the exact value of the expression. -cos (-390°)

Find the exact value of the expression. -csc 840°

Evaluate. - $\sin ^ { 2 } 45 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ }$

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -cos ϴ = 0.49566425

Evaluate. - $5 \sin ^ { 2 } 300 ^ { \circ } + \csc ^ { 2 } 150 ^ { \circ } - \sec ^ { 2 } 30 ^ { \circ }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -csc 35°

Solve the problem. -From the top of a vertical tower, 319 feet above the the surface of the earth, the angle of depression to a doghouse is 23° 3´. How far is it from the doghouse to the foot of the tower? Round your Answer to the hundredths place when necessary.

Determine whether the statement is true or false. -sin 60° = 2 sin 30°

Find the sign of the following. - $\sin \frac { \theta } { 2 }$ , given that $\theta$ is in the interval $\left( 180 ^ { \circ } , 270 ^ { \circ } \right)$ .

Solve the problem. -Find the exact value of x in the figure.

Find the exact value of the expression. -sin 30°

Find the exact value of the expression. -cot 60°

Solve the problem. -A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 14.1 miles due south of A, is N 32°57'W. How far is the fire from B (to the nearest tenth of a mile)?

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\frac { 1 } { \tan 38 ^ { \circ } 46 ^ { \prime } }$

Trigonometric Functions

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 2: Acute Angles and Right Triangles

Without using a calculator, give the exact trigonometric function value with rational denominator. - tan⁡45∘\tan 45 ^ { \circ }tan45∘