Question 1

Determine whether the statement is true or false.
-$$\cos 60 ^ { \circ } = 1 - 2 \sin ^ { 2 } 30 ^ { \circ }$$

Accepted Answer

A) True 
 B)False

Question 2

Solve the problem.
-From a balloon 1037 feet high, the angle of depression to the ranger headquarters is 58°41'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Accepted Answer

A) 626 ft 
B) 621 ft 
C) 636 ft 
D) 631 ft

Question 3

Solve the problem.
-Find a formula for the area of the figure in terms of s.

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 } \mathrm {~s} ^ { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 2 } s ^ { 2 }$ 
C)  $\frac { \sqrt { s } } { 3 }$ 
D)  $\frac { \sqrt { 3 } } { 6 } \mathrm {~s} ^ { 2 }$

Question 4

Find a solution for the equation. Assume that all angles are acute angles.
-sin A = cos 8A

Accepted Answer

A) 8° 
B) 82° 
C) 10° 
D) 80°

Question 5

Solve the problem.
-A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed, the angle of depression to the car is 26° 53´. When the car
Stops, the angle of depression is 42° 31´. The building is 240 feet tall. How far did the car travel from
When it was first noticed until it stopped? Round to the nearest foot.

Accepted Answer

A) 212 ft 
B) 412 ft 
C) 238 ft 
D) 191 ft

Question 6

Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$-axis is $\frac { \sqrt { 3 } } { 2 }$.

Accepted Answer

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

Question 7

Find the reference angle for the given angle.
--403°

Accepted Answer

A) 47° 
B) 137° 
C) 43° 
D) 133°

Question 8

Evaluate the function requested. Write your answer as a fraction in lowest terms.
-
Find $\sin \mathrm { A }$.

Accepted Answer

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

Question 9

Solve the problem.
-Any offset between a stationary radar gun and a moving target creates a "cosine effect" that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the
Radar speed reading is the product of the actual reading and the cosine of the angle. Find the radar
Reading to the nearest hundredth for the auto shown in the figure.

Accepted Answer

A)  $21.82 \mathrm { mph }$ 
B)  $97.97 \mathrm { mph }$ 
C)  $94.51 \mathrm { mph }$ 
D)  $96.03 \mathrm { mph }$

Question 10

Solve the problem.
-A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 13° 12´. When the boat stops, the
Angle of depression is 49° 49´. The lighthouse is 200 feet tall. How far did the boat travel from when
It was first noticed until it stopped? Round to the nearest foot.

Accepted Answer

A) 706 ft 
B) 668 ft 
C) 729 ft 
D) 684 ft

Question 11

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-sin 304°53´

Accepted Answer

A) -0.8103183 
B) -0.8203183 
C) -0.8213183 
D) -0.8303183

Question 12

Without using a calculator, give the exact trigonometric function value with rational denominator.
-cos 60°

Accepted Answer

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

Question 13

Find a solution for the equation. Assume that all angles are acute angles.
-$$\tan \left( 3 \alpha + 12 ^ { \circ } \right) = \cot \left( \alpha + 36 ^ { \circ } \right)$$

Accepted Answer

A)  $10.5 ^ { \circ }$ 
B)  $16 ^ { \circ }$ 
C)  $14.5 ^ { \circ }$ 
D)  $12 ^ { \circ }$

Question 14

The number represents an approximate measurement. State the range represented by the measurement.
-21 ft

Accepted Answer

A) 20.5 ft to 21.5 ft 
B) 20.75 ft to 21.25 ft 
C) 20.9 ft to 21.1 ft 
D) 20 ft to 22 ft

Question 15

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

Accepted Answer

A)  $\frac { 74 \sqrt { 3 } } { 3 }$ 
B)  $79 \sqrt { 6 }$ 
C)  $\frac { 20 \sqrt { 6 } } { 3 }$ 
D)  $\frac { 80 \sqrt { 6 } } { 3 }$

Question 16

Evaluate the function requested. Write your answer as a fraction in lowest terms.
-
Find $\tan \mathrm { A }$.

Accepted Answer

A)  $\tan \mathrm { A } = \frac { 5 } { 13 }$ 
B)  $\tan \mathrm { A } = \frac { 5 } { 12 }$ 
C)  $\tan \mathrm { A } = \frac { 13 } { 5 }$ 
D)  $\tan \mathrm { A } = \frac { 12 } { 5 }$

Question 17

Solve the problem.
-A 37-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 16´ with the side of the building, how far up from the ground does the ladder make contact with
The building? Round your answer to the hundredths place when necessary.

Accepted Answer

A) 36.89 ft 
B) 34.93 ft 
C) 33.73 ft 
D) 31.16 ft

Question 18

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-sin ϴ = 0.81107642

Accepted Answer

A) 54.2012343° 
B) 35.7987657° 
C) 125.798766° 
D) 234.201234°

Question 19

Solve the problem.
-Snell's Law states that $\frac { c _ { 1 } } { c _ { 2 } } = \frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } }$. Use this law to find the requested value. If $c _ { 1 } = 6 \times 10 ^ { 8 }$, $c _ { 2 } = 4.66 \times 10 ^ { 8 } , \theta _ { 1 } = 43 ^ { \circ }$, find $\theta _ { 2 }$. Round your answer to the nearest degree.

Accepted Answer

A)  $\theta _ { 2 } = 31 ^ { \circ }$ 
B)  $\theta _ { 2 } = 34 ^ { \circ }$ 
C)  $\theta _ { 2 } = 32 ^ { \circ }$ 
D)  $\theta _ { 2 } = 35 ^ { \circ }$

Question 20

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$$\sin ^ { 2 } 57 ^ { \circ } + \cos ^ { 2 } 57 ^ { \circ }$$

Accepted Answer

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

Exam 2: Acute Angles and Right Triangles

Determine whether the statement is true or false. - $\cos 60 ^ { \circ } = 1 - 2 \sin ^ { 2 } 30 ^ { \circ }$

Solve the problem. -From a balloon 1037 feet high, the angle of depression to the ranger headquarters is 58°41'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot) ?

Find a solution for the equation. Assume that all angles are acute angles. -sin A = cos 8A

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

Find the reference angle for the given angle. --403°

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -sin 304°53´

Without using a calculator, give the exact trigonometric function value with rational denominator. -cos 60°

Find a solution for the equation. Assume that all angles are acute angles. - $\tan \left( 3 \alpha + 12 ^ { \circ } \right) = \cot \left( \alpha + 36 ^ { \circ } \right)$

The number represents an approximate measurement. State the range represented by the measurement. -21 ft

Solve the problem. -Find the exact value of x in the figure. $Solve the problem. -Find the exact value of x in the figure. A) \frac { 74 \sqrt { 3 } } { 3 } B) 79 \sqrt { 6 } C) \frac { 20 \sqrt { 6 } } { 3 } D) \frac { 80 \sqrt { 6 } } { 3 }$

Solve the problem. -A 37-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 16´ with the side of the building, how far up from the ground does the ladder make contact with The building? Round your answer to the hundredths place when necessary.

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -sin ϴ = 0.81107642

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sin ^ { 2 } 57 ^ { \circ } + \cos ^ { 2 } 57 ^ { \circ }$

Exam 2: Acute Angles and Right Triangles

Determine whether the statement is true or false. - cos⁡60∘=1−2sin⁡230∘\cos 60 ^ { \circ } = 1 - 2 \sin ^ { 2 } 30 ^ { \circ }cos60∘=1−2sin230∘

Solve the problem. -From a balloon 1037 feet high, the angle of depression to the ranger headquarters is 58°41'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot) ?

Solve the problem. -Find a formula for the area of the figure in terms of s.

Find a solution for the equation. Assume that all angles are acute angles. -sin A = cos 8A

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant III and the positive xxx -axis is 32\frac { \sqrt { 3 } } { 2 }23​​ .

Find the reference angle for the given angle. --403°

Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find sin⁡A\sin \mathrm { A }sinA .