Question 1

Without using a calculator, give the exact trigonometric function value with rational denominator.
-sin 45°

Accepted Answer

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

Question 2

State in which quadrant the terminal side of the given angle lies.
--671°

Accepted Answer

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

Question 3

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-160°

Accepted Answer

A)  $340 ^ { \circ }$ and $- 20 ^ { \circ }$
  
B)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
C)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
D)  $340^{\circ} \text { and }-20^{\circ}$
  
A)  $340 ^ { \circ }$ and $- 20 ^ { \circ }$
  
B)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
C)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
D)  $340^{\circ} \text { and }-20^{\circ}$

Question 4

Write the expression in terms of its cofunction.
-cos 18°

Accepted Answer

A) sin 18° 
B) sec 18° 
C) csc 72° 
D) sin 72° 
A) sin 18° 
B) sec 18° 
C) csc 72° 
D) sin 72°

Question 5

Use a calculator to find the function value to four decimal places.
-tan 74°42'

Accepted Answer

A) 3.6563 
B) 3.6554 
C) 3.6557 
D) 3.656 
A) 3.6563 
B) 3.6554 
C) 3.6557 
D) 3.656

Question 6

Complement of 82.1°

Accepted Answer

A) 97.9° 
B) 187.9° 
C) 7.9° 
D) 277.9° 
A) 97.9° 
B) 187.9° 
C) 7.9° 
D) 277.9°

Question 7

Supplement of 66°

Accepted Answer

A) 294° 
B) 132° 
C) 114° 
D) 24° 
A) 294° 
B) 132° 
C) 114° 
D) 24°

Question 8

Write the expression in terms of its cofunction.
-cos 74°35'

Accepted Answer

A) sin 15°25' 
B) sin 15°65' 
C) sin 105°25' 
D) sin 16°25' 
A) sin 15°25' 
B) sin 15°65' 
C) sin 105°25' 
D) sin 16°25'

Question 9

Use the fundamental identities to find the value of the trigonometric function.
-$\sec \beta$, if $\sin \beta = - \frac { 5 } { 11 }$, with $\beta$ in quadrant III

Accepted Answer

A)  $- \frac { 4 \sqrt { 6 } } { 11 }$ 
B)  $- \frac { 5 \sqrt { 6 } } { 24 }$ 
C)  $\frac { \sqrt { 11 } } { 5 }$ 
D)  $- \frac { 11 \sqrt { 6 } } { 24 }$ 
A)  $- \frac { 4 \sqrt { 6 } } { 11 }$ 
B)  $- \frac { 5 \sqrt { 6 } } { 24 }$ 
C)  $\frac { \sqrt { 11 } } { 5 }$ 
D)  $- \frac { 11 \sqrt { 6 } } { 24 }$

Question 10

State in which quadrant the terminal side of the given angle lies.
--7.8°

Accepted Answer

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

Question 11

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\csc \theta = - \frac { 2 \sqrt { 3 } } { 3 }$

Accepted Answer

A)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
B)  $150 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $240 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $120 ^ { \circ }$ and $300 ^ { \circ }$ 
A)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
B)  $150 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $240 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $120 ^ { \circ }$ and $300 ^ { \circ }$

Question 12

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-10°

Accepted Answer

A)  $370 ^ { \circ }$ and $- 350 ^ { \circ }$
  
B)  $370 ^ { \circ }$ and $- 350 ^ { \circ }$
  
C)  $190 ^ { \circ }$ and $- 170 ^ { \circ }$
  
D)  $190 ^ { \circ }$ and $- 170 ^ { \circ }$
  
A)  $370 ^ { \circ }$ and $- 350 ^ { \circ }$
  
B)  $370 ^ { \circ }$ and $- 350 ^ { \circ }$
  
C)  $190 ^ { \circ }$ and $- 170 ^ { \circ }$
  
D)  $190 ^ { \circ }$ and $- 170 ^ { \circ }$

Question 13

Solve the right triangle.
-a = 3.5 m, B = 25.9°, C = 90°

Accepted Answer

A) A = 64.1°, b = 3.8 m, c = 5.2 m 
B) A = 64.1°, b = 3.8 m, c = 3.9 m 
C) A = 64.1°, b = 0.6 m, c = 3.6 m 
D) A = 64.1°, b = 1.7 m, c = 3.9 m 
A) A = 64.1°, b = 3.8 m, c = 5.2 m 
B) A = 64.1°, b = 3.8 m, c = 3.9 m 
C) A = 64.1°, b = 0.6 m, c = 3.6 m 
D) A = 64.1°, b = 1.7 m, c = 3.9 m

Question 14

$\sin \left( 750 ^ { \circ } \right)$

Accepted Answer

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

Question 15

Sketch an angle $\theta$ in standard position such that $\theta$ has the smallest possible positive measure and the given point is on the terminal side of $\theta$.
-P = (1, 3)

Accepted Answer

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

Question 16

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions.
-$\cot \theta  0$

Accepted Answer

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

Question 17

When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36°2'. If Joey is known to be standing 21 feet from the base of the tree, how tall is the tree (to
The nearest foot)?

Accepted Answer

A) 17 ft 
B) 15 ft 
C) 19 ft 
D) 21 ft 
A) 17 ft 
B) 15 ft 
C) 19 ft 
D) 21 ft

Question 18

Solve the right triangle.
-A = 11° 17', c = 289 ft, C = 90°

Accepted Answer

A) B = 79° 42', a = 56.55 ft, b = 279.41 ft 
B) B = 78° 42', a = 59.75 ft, b = 284.61 ft 
C) B = 78° 43', a = 55.98 ft , b = 282.52 ft 
D) B = 78° 43', a = 56.55 ft, b = 283.41 ft 
A) B = 79° 42', a = 56.55 ft, b = 279.41 ft 
B) B = 78° 42', a = 59.75 ft, b = 284.61 ft 
C) B = 78° 43', a = 55.98 ft , b = 282.52 ft 
D) B = 78° 43', a = 56.55 ft, b = 283.41 ft

Question 19

Sketch an angle $\theta$ in standard position such that $\theta$ has the smallest possible positive measure and the given point is on the terminal side of $\theta$.
-P = (4, -2)

Accepted Answer

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

Question 20

Find the exact value of the function. Rationalize the denominator if necessary.
-tan 330°

Accepted Answer

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

Without using a calculator, give the exact trigonometric function value with rational denominator. -sin 45°

State in which quadrant the terminal side of the given angle lies. --671°

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -160°

Write the expression in terms of its cofunction. -cos 18°

Use a calculator to find the function value to four decimal places. -tan 74°42'

Complement of 82.1°

Supplement of 66°

Write the expression in terms of its cofunction. -cos 74°35'

Use the fundamental identities to find the value of the trigonometric function. - $\sec \beta$ , if $\sin \beta = - \frac { 5 } { 11 }$ , with $\beta$ in quadrant III

State in which quadrant the terminal side of the given angle lies. --7.8°

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ - $\csc \theta = - \frac { 2 \sqrt { 3 } } { 3 }$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -10°

Solve the right triangle. -a = 3.5 m, B = 25.9°, C = 90°

$\sin \left( 750 ^ { \circ } \right)$

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\cot \theta < 0$ and $\cos \theta > 0$

When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36°2'. If Joey is known to be standing 21 feet from the base of the tree, how tall is the tree (to The nearest foot)?

Solve the right triangle. -A = 11° 17', c = 289 ft, C = 90°

Find the exact value of the function. Rationalize the denominator if necessary. -tan 330°

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Exam 14: Trigonometry Formerly

Without using a calculator, give the exact trigonometric function value with rational denominator. -sin 45°

State in which quadrant the terminal side of the given angle lies. --671°

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -160°

Write the expression in terms of its cofunction. -cos 18°

Use a calculator to find the function value to four decimal places. -tan 74°42'

Complement of 82.1°

Supplement of 66°

Write the expression in terms of its cofunction. -cos 74°35'

Use the fundamental identities to find the value of the trigonometric function. - sec⁡β\sec \betasecβ , if sin⁡β=−511\sin \beta = - \frac { 5 } { 11 }sinβ=−115​ , with β\betaβ in quadrant III

State in which quadrant the terminal side of the given angle lies. --7.8°

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -10°

Solve the right triangle. -a = 3.5 m, B = 25.9°, C = 90°

sin⁡(750∘)\sin \left( 750 ^ { \circ } \right)sin(750∘)

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the smallest possible positive measure and the given point is on the terminal side of θ\thetaθ . -P = (1, 3)

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - cot⁡θ<0\cot \theta < 0cotθ<0 and cos⁡θ>0\cos \theta > 0cosθ>0

When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36°2'. If Joey is known to be standing 21 feet from the base of the tree, how tall is the tree (to The nearest foot)?

Solve the right triangle. -A = 11° 17', c = 289 ft, C = 90°

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the smallest possible positive measure and the given point is on the terminal side of θ\thetaθ . -P = (4, -2)

Find the exact value of the function. Rationalize the denominator if necessary. -tan 330°

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

Use the fundamental identities to find the value of the trigonometric function. - $\sec \beta$ , if $\sin \beta = - \frac { 5 } { 11 }$ , with $\beta$ in quadrant III

$\sin \left( 750 ^ { \circ } \right)$

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\cot \theta < 0$ and $\cos \theta > 0$