Question 1

Find the sign of the following.
-cot (ϴ + 180°), given that ϴ is in the interval (270°, 360°).

Accepted Answer

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

Question 2

Determine whether the statement is true or false.
-cos 195° = 2 cos 225° cos 30° + 2 sin 225° sin 30°

Accepted Answer

A) True 
 B)False

Question 3

Find the sign of the following.
-cos (ϴ + 180°), given that ϴ is in the interval (90°, 180°).

Accepted Answer

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

Question 4

Evaluate.
-$\cot ^ { 2 } 45 ^ { \circ } + \sin 150 ^ { \circ } + 4 \tan ^ { 2 } 45 ^ { \circ }$

Accepted Answer

A)  $\frac { 7 } { 2 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $\frac { 11 } { 2 }$ 
A)  $\frac { 7 } { 2 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $\frac { 11 } { 2 }$

Question 5

Solve the problem.
-A 5.6-ft fence is 12.818 ft away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing)Find ϴ, the angle of
Elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree
When necessary.

Accepted Answer

A)  $\theta = 25 ^ { \circ }$ 
B)  $\theta = 23.8 ^ { \circ }$ 
C)  $\theta = 23.6 ^ { \circ }$ 
D)  $\theta = 23.4 ^ { \circ }$ 
A)  $\theta = 25 ^ { \circ }$ 
B)  $\theta = 23.8 ^ { \circ }$ 
C)  $\theta = 23.6 ^ { \circ }$ 
D)  $\theta = 23.4 ^ { \circ }$

Question 6

Determine whether the statement is true or false.
-cos 30° + cos 45° = cos 75°

Accepted Answer

A) True 
 B)False

Question 7

Solve the problem.
-Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 21° 32´. He then
Drives 1 mile (1 mile = 5280 ft)more and measures the angle of elevation to be 35° 7´. Find the
Height of the mountain to the nearest foot.

Accepted Answer

A) 4847 ft 
B) 47,467 ft 
C) 474,672 ft 
D) 4747 ft 
A) 4847 ft 
B) 47,467 ft 
C) 474,672 ft 
D) 4747 ft

Question 8

Solve the right triangle.
-$$\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 63.4 ^ { \circ } , \mathrm { B } = 26.6 ^ { \circ } , \mathrm { c } = 2.9 \mathrm {~cm}$ 
B)  $\mathrm { A } = 30.0 ^ { \circ } , \mathrm { B } = 60.0 ^ { \circ } , \mathrm { c } = 3.9 \mathrm {~cm}$ 
C)  $\mathrm { A } = 26.6 ^ { \circ } , \mathrm { B } = 63.4 ^ { \circ } , \mathrm { C } = 2.9 \mathrm {~cm}$ 
D)  $\mathrm { A } = 58.9 ^ { \circ } , \mathrm { B } = 31.1 ^ { \circ } , \mathrm { C } = 2.9 \mathrm {~cm}$ 
A)  $\mathrm { A } = 63.4 ^ { \circ } , \mathrm { B } = 26.6 ^ { \circ } , \mathrm { c } = 2.9 \mathrm {~cm}$ 
B)  $\mathrm { A } = 30.0 ^ { \circ } , \mathrm { B } = 60.0 ^ { \circ } , \mathrm { c } = 3.9 \mathrm {~cm}$ 
C)  $\mathrm { A } = 26.6 ^ { \circ } , \mathrm { B } = 63.4 ^ { \circ } , \mathrm { C } = 2.9 \mathrm {~cm}$ 
D)  $\mathrm { A } = 58.9 ^ { \circ } , \mathrm { B } = 31.1 ^ { \circ } , \mathrm { C } = 2.9 \mathrm {~cm}$

Question 9

Use a calculator to decide whether the statement is true or false.
-$$\cos \left( 2 \cdot 90 ^ { \circ } \right) = \cos ^ { 2 } 90 ^ { \circ } - \sin ^ { 2 } 90 ^ { \circ }$$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 10

Find the reference angle for the given angle.
-129°

Accepted Answer

A) 51° 
B) 49° 
C) 39° 
D) 61° 
A) 51° 
B) 49° 
C) 39° 
D) 61°

Question 11

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 $\csc A$ when $b = 24$ and $c = 51$

Accepted Answer

A)  $\frac { 8 } { 15 }$ 
B)  $\frac { 17 } { 15 }$ 
C)  $\frac { 15 } { 17 }$ 
D)  $\frac { 17 } { 8 }$ 
A)  $\frac { 8 } { 15 }$ 
B)  $\frac { 17 } { 15 }$ 
C)  $\frac { 15 } { 17 }$ 
D)  $\frac { 17 } { 8 }$

Question 12

Use a calculator to decide whether the statement is true or false.
-sin (150° + 30°)= sin 150° + sin 30°

Accepted Answer

A) True 
 B)False

Question 13

Solve the problem.
-If an automobile is traveling at velocity $\mathrm { V }$ (in feet per second), the safe radius $\mathrm { R }$ for a curve with superelevation $\alpha$ is given by the formula $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$, where $\mathrm { f }$ and $g$ are constants. A road is being constructed for automobiles traveling at 50 miles per hour. If $\alpha = 4 ^ { \circ } , \mathrm { g } = 32.4$, and $\mathrm { f } = 0.16$, calculate R. Round to the nearest foot. (Hint: 1 mile $= 5280$ feet)

Accepted Answer

A)  $R = 1172 \mathrm { ft }$ 
B)  $R = 706 \mathrm { ft }$ 
C)  $R = 722 \mathrm { ft }$ 
D)  $\mathrm { R } = 742 \mathrm { ft }$ 
A)  $R = 1172 \mathrm { ft }$ 
B)  $R = 706 \mathrm { ft }$ 
C)  $R = 722 \mathrm { ft }$ 
D)  $\mathrm { R } = 742 \mathrm { ft }$

Question 14

Solve the problem.
-In one area, the lowest angle of elevation of the sun in winter is 29° 8´. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to
The tenths place when necessary.

Accepted Answer

A)  $8.6 \mathrm { ft }$ 
B)  $9 \mathrm { ft }$ 
C)  $12.4 \mathrm { ft }$ 
D)  $9.2 \mathrm { ft }$ 
A)  $8.6 \mathrm { ft }$ 
B)  $9 \mathrm { ft }$ 
C)  $12.4 \mathrm { ft }$ 
D)  $9.2 \mathrm { ft }$

Question 15

Solve the right triangle.
-B = 25.9°, c = 4.1 mm, C = 90° Round values to one decimal place.

Accepted Answer

A) a = 3.7 mm, A = 64.1°, b = 1.8 mm 
B) a = 3.7 mm, A = 64.1°, b = 2.9 mm 
C) a = 1.8 mm, A = 64.1°, b = 3.7 mm 
D) a = 2.9 mm, A = 64.1°, b = 2.9 mm 
A) a = 3.7 mm, A = 64.1°, b = 1.8 mm 
B) a = 3.7 mm, A = 64.1°, b = 2.9 mm 
C) a = 1.8 mm, A = 64.1°, b = 3.7 mm 
D) a = 2.9 mm, A = 64.1°, b = 2.9 mm

Question 16

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 $\csc \mathrm { B }$ when $\mathrm { a } = 6$ and $\mathrm { b } = 7$

Accepted Answer

A)  $\frac { \sqrt { 85 } } { 7 }$ 
B)  $\frac { 7 \sqrt { 85 } } { 85 }$ 
C)  $\frac { \sqrt { 85 } } { 6 }$ 
D)  $\frac { 6 \sqrt { 85 } } { 85 }$ 
A)  $\frac { \sqrt { 85 } } { 7 }$ 
B)  $\frac { 7 \sqrt { 85 } } { 85 }$ 
C)  $\frac { \sqrt { 85 } } { 6 }$ 
D)  $\frac { 6 \sqrt { 85 } } { 85 }$

Question 17

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

Accepted Answer

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

Question 18

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-cos 39° 5' cos 50° 55' - sin 39° 5' sin 50° 55'

Accepted Answer

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

Question 19

Find the exact value of the expression.
-sec 3105°

Accepted Answer

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

Question 20

Evaluate the function requested. Write your answer as a fraction in lowest terms.
- 
Find $\cos B$.

Accepted Answer

A)  $\cos B = \frac { 9 } { 40 }$ 
B)  $\cos B = \frac { 40 } { 41 }$ 
C)  $\cos B = \frac { 9 } { 41 }$ 
D)  $\cos B = \frac { 41 } { 40 }$ 
A)  $\cos B = \frac { 9 } { 40 }$ 
B)  $\cos B = \frac { 40 } { 41 }$ 
C)  $\cos B = \frac { 9 } { 41 }$ 
D)  $\cos B = \frac { 41 } { 40 }$

Find the sign of the following. -cot (ϴ + 180°), given that ϴ is in the interval (270°, 360°).

Determine whether the statement is true or false. -cos 195° = 2 cos 225° cos 30° + 2 sin 225° sin 30°

Find the sign of the following. -cos (ϴ + 180°), given that ϴ is in the interval (90°, 180°).

Evaluate. - $\cot ^ { 2 } 45 ^ { \circ } + \sin 150 ^ { \circ } + 4 \tan ^ { 2 } 45 ^ { \circ }$

Determine whether the statement is true or false. -cos 30° + cos 45° = cos 75°

Solve the right triangle. - $\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Use a calculator to decide whether the statement is true or false. - $\cos \left( 2 \cdot 90 ^ { \circ } \right) = \cos ^ { 2 } 90 ^ { \circ } - \sin ^ { 2 } 90 ^ { \circ }$

Find the reference angle for the given angle. -129°

Use a calculator to decide whether the statement is true or false. -sin (150° + 30°)= sin 150° + sin 30°

Solve the problem. -In one area, the lowest angle of elevation of the sun in winter is 29° 8´. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to The tenths place when necessary.

Solve the right triangle. -B = 25.9°, c = 4.1 mm, C = 90° Round values to one decimal place.

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

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cos 39° 5' cos 50° 55' - sin 39° 5' sin 50° 55'

Find the exact value of the expression. -sec 3105°

Evaluate the function requested. Write your answer as a fraction in lowest terms. - $Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find \cos B .$ Find $\cos B$ .

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

Find the sign of the following. -cot (ϴ + 180°), given that ϴ is in the interval (270°, 360°).

Determine whether the statement is true or false. -cos 195° = 2 cos 225° cos 30° + 2 sin 225° sin 30°

Find the sign of the following. -cos (ϴ + 180°), given that ϴ is in the interval (90°, 180°).

Evaluate. - cot⁡245∘+sin⁡150∘+4tan⁡245∘\cot ^ { 2 } 45 ^ { \circ } + \sin 150 ^ { \circ } + 4 \tan ^ { 2 } 45 ^ { \circ }cot245∘+sin150∘+4tan245∘

Determine whether the statement is true or false. -cos 30° + cos 45° = cos 75°

Solve the right triangle. - a=2.6 cm, b=1.3 cm,C=90∘\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }a=2.6 cm, b=1.3 cm,C=90∘ Round values to one decimal place.

Use a calculator to decide whether the statement is true or false. - cos⁡(2⋅90∘)=cos⁡290∘−sin⁡290∘\cos \left( 2 \cdot 90 ^ { \circ } \right) = \cos ^ { 2 } 90 ^ { \circ } - \sin ^ { 2 } 90 ^ { \circ }cos(2⋅90∘)=cos290∘−sin290∘

Find the reference angle for the given angle. -129°

Use a calculator to decide whether the statement is true or false. -sin (150° + 30°)= sin 150° + sin 30°

Solve the problem. -In one area, the lowest angle of elevation of the sun in winter is 29° 8´. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to The tenths place when necessary.

Solve the right triangle. -B = 25.9°, c = 4.1 mm, C = 90° Round values to one decimal place.

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

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cos 39° 5' cos 50° 55' - sin 39° 5' sin 50° 55'

Find the exact value of the expression. -sec 3105°

Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find cos⁡B\cos BcosB .

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

Evaluate. - $\cot ^ { 2 } 45 ^ { \circ } + \sin 150 ^ { \circ } + 4 \tan ^ { 2 } 45 ^ { \circ }$

Solve the right triangle. - $\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Use a calculator to decide whether the statement is true or false. - $\cos \left( 2 \cdot 90 ^ { \circ } \right) = \cos ^ { 2 } 90 ^ { \circ } - \sin ^ { 2 } 90 ^ { \circ }$

Evaluate the function requested. Write your answer as a fraction in lowest terms. - $Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find \cos B .$ Find $\cos B$ .