Question 1

Determine the exact value of $\cot \theta$ when $\cos \theta = \frac { 3 } { 5 }$ and $\cot \theta > 0$ .

Accepted Answer

A)  $\cot \theta = \frac { 3 } { 4 }$ 
B)  $\cot \theta = \frac { 4 } { 3 }$ 
C)  $\cot \theta = \frac { 3 } { 2 }$ 
D)  $\cot \theta = \frac { 7 } { 4 }$ 
E)  $\cot \theta = \frac { 2 } { 3 }$ 
A)  $\cot \theta = \frac { 3 } { 4 }$ 
B)  $\cot \theta = \frac { 4 } { 3 }$ 
C)  $\cot \theta = \frac { 3 } { 2 }$ 
D)  $\cot \theta = \frac { 7 } { 4 }$ 
E)  $\cot \theta = \frac { 2 } { 3 }$

Question 2

The terminal side of θ lies on the line $- 15 x - 8 y = 0$ in the fourth quadrant.Find the exact value of $\cos \theta$ .

Accepted Answer

A)  $\cos \theta = \frac { 8 } { 17 }$ 
B)  $\cos \theta = \frac { 8 } { 25 }$ 
C)  $\cos \theta = \frac { 25 } { 52 }$ 
D)  $\cos \theta = \frac { 17 } { 8 }$ 
E)  $\cos \theta = \frac { 25 } { 17 }$ 
A)  $\cos \theta = \frac { 8 } { 17 }$ 
B)  $\cos \theta = \frac { 8 } { 25 }$ 
C)  $\cos \theta = \frac { 25 } { 52 }$ 
D)  $\cos \theta = \frac { 17 } { 8 }$ 
E)  $\cos \theta = \frac { 25 } { 17 }$

Question 3

Evaluate the trigonometric function.Round your answer to four decimal places. ​
Cot 171°
​

Accepted Answer

A) -5.3138 
B) -4.3138 
C) -6.3138 
D) -3.3138 
E) -5.8138 
A) -5.3138 
B) -4.3138 
C) -6.3138 
D) -3.3138 
E) -5.8138

Question 4

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = 4 \cos ( 8 t )$ ,where y is the displacement in centimeters and t is the time in seconds.Find the displacement when $t = 1.25$ ,rounding your answer to four decimal places. ​

Accepted Answer

A) 2.2693 cm 
B) -3.3563 cm 
C) -0.7275 cm 
D) -6.5364 cm 
E) 10.0903 cm 
A) 2.2693 cm 
B) -3.3563 cm 
C) -0.7275 cm 
D) -6.5364 cm 
E) 10.0903 cm

Question 5

The point (7,24)is on the terminal side of an angle in standard position.Determine the exact value of cos θ.

Accepted Answer

A)  $\cot \theta = - \frac { 24 } { 7 }$ 
B)  $\cot \theta = \frac { 24 } { 25 }$ 
C)  $\cot \theta = \frac { 25 } { 24 }$ 
D)  $\cot \theta = - \frac { 24 } { 25 }$ 
E)  $\cot \theta = - \frac { 7 } { 24 }$ 
A)  $\cot \theta = - \frac { 24 } { 7 }$ 
B)  $\cot \theta = \frac { 24 } { 25 }$ 
C)  $\cot \theta = \frac { 25 } { 24 }$ 
D)  $\cot \theta = - \frac { 24 } { 25 }$ 
E)  $\cot \theta = - \frac { 7 } { 24 }$

Question 6

Given the equation below,determine two solutions such that $0 < \theta < 2 \pi$ . sec​ θ = $\frac { 2 \sqrt { 3 } } { 3 }$ ​

Accepted Answer

A)  $\theta = \frac { \pi } { 6 }$ 
B)  $\theta = \frac { 11 \pi } { 8 } , \frac { 7 \pi } { 8 }$ 
C)  $\theta = \frac { 2 \pi } { 4 } , \frac { 5 \pi } { 8 }$ 
D) ​ $\theta = \frac { 2 \pi } { 3 } , \frac { \pi } { 3 }$ 
E)  $\theta = \frac { 11 \pi } { 6 } , \frac { \pi } { 6 }$ 
A)  $\theta = \frac { \pi } { 6 }$ 
B)  $\theta = \frac { 11 \pi } { 8 } , \frac { 7 \pi } { 8 }$ 
C)  $\theta = \frac { 2 \pi } { 4 } , \frac { 5 \pi } { 8 }$ 
D) ​ $\theta = \frac { 2 \pi } { 3 } , \frac { \pi } { 3 }$ 
E)  $\theta = \frac { 11 \pi } { 6 } , \frac { \pi } { 6 }$

Question 7

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. )​ $\cos ( - 1180 )$ ​

Accepted Answer

A) -0.1736 
B) 0.3264 
C) -0.0736 
D) 0.1264 
E) 0.2264 
A) -0.1736 
B) 0.3264 
C) -0.0736 
D) 0.1264 
E) 0.2264

Question 8

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) ​
Tan 306°
​

Accepted Answer

A) -1.0764 
B) -1.2764 
C) -1.3764 
D) -0.8764 
E) -0.9764 
A) -1.0764 
B) -1.2764 
C) -1.3764 
D) -0.8764 
E) -0.9764

Question 9

Find the reference angle $\theta^\prime$ ,and $\theta$ sketch and $\theta^\prime$ in standard position.​ $\theta = 160 ^ { \circ }$ ​

Accepted Answer

A)  $\theta ^ { \prime } = 10 ^ { \circ }$   
B)  $\theta^\prime = 30 ^ { \circ }$   
C)  $\theta ^ { \prime } = - 20 ^ { \circ }$   
D)  $\theta ^ { \prime } = 20 ^ { \circ }$   
E)  $\theta ^ { \prime } = 40 ^ { \circ }$   
A)  $\theta ^ { \prime } = 10 ^ { \circ }$   
B)  $\theta^\prime = 30 ^ { \circ }$   
C)  $\theta ^ { \prime } = - 20 ^ { \circ }$   
D)  $\theta ^ { \prime } = 20 ^ { \circ }$   
E)  $\theta ^ { \prime } = 40 ^ { \circ }$

Question 10

Determine the exact values of the three trigonometric functions csc,sec,and cot of the angle θ.​   ​ where a = 15 and b = 8.
​

Accepted Answer

A) csc θ = - $$\frac { 17 } { 8 }$$ sec θ = - $\frac { 17 } { 15 }$
Cot θ = $\frac { 15 } { 8 }$ 
B) cscθ = - $\frac { 17 } { 8 }$ sec θ = - $\frac { 15 } { 8 }$
Cot θ = - $\frac { 17 } { 15 }$ 
C) csc θ = - $\frac { 17 } { 8 }$ sec θ = - $\frac { 17 } { 15 }$
Cot θ = - $\frac { 17 } { 8 }$ 
D) csc θ = - $\frac { 15 } { 8 }$ sec θ = - $\frac { 17 } { 15 }$
Cot θ = - $\frac { 17 } { 8 }$ 
E) csc θ = - $\frac { 17 } { 15 }$ sec θ = - $\frac { 17 } { 8 }$
Cot θ = - $\frac { 15 } { 8 }$ 
A) csc θ = - $$\frac { 17 } { 8 }$$ sec θ = - $\frac { 17 } { 15 }$
Cot θ = $\frac { 15 } { 8 }$ 
B) cscθ = - $\frac { 17 } { 8 }$ sec θ = - $\frac { 15 } { 8 }$
Cot θ = - $\frac { 17 } { 15 }$ 
C) csc θ = - $\frac { 17 } { 8 }$ sec θ = - $\frac { 17 } { 15 }$
Cot θ = - $\frac { 17 } { 8 }$ 
D) csc θ = - $\frac { 15 } { 8 }$ sec θ = - $\frac { 17 } { 15 }$
Cot θ = - $\frac { 17 } { 8 }$ 
E) csc θ = - $\frac { 17 } { 15 }$ sec θ = - $\frac { 17 } { 8 }$
Cot θ = - $\frac { 15 } { 8 }$

Question 11

Evaluate the trigonometric function.Round your answer to four decimal places. ​
Tan ( -187°)
​

Accepted Answer

A) 0.8772 
B) 1.8772 
C) -0.1228 
D) 2.8772 
E) 0.3772 
A) 0.8772 
B) 1.8772 
C) -0.1228 
D) 2.8772 
E) 0.3772

Question 12

Evaluate the trigonometric function.Round your answer to four decimal places.​ $$\csc \left( - \frac { 13 \pi } { 12 } \right)$$ ​

Accepted Answer

A) 1.8637 
B) 3.8637 
C) 4.3637 
D) 6.8637 
E) 4.8637 
A) 1.8637 
B) 3.8637 
C) 4.3637 
D) 6.8637 
E) 4.8637

Question 13

Determine the exact value of $\sin \left( - 225 ^ { \circ } \right)$ .

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\frac { \sqrt { 5 } } { 2 }$ 
C)  $- \frac { \sqrt { 2 } } { 2 }$ 
D) 1 
E) -1 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\frac { \sqrt { 5 } } { 2 }$ 
C)  $- \frac { \sqrt { 2 } } { 2 }$ 
D) 1 
E) -1

Question 14

Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ.​   ​ where $a = 12 \text { and } b = 5$ ​

Accepted Answer

A) sin θ = - $\frac { 5 } { 13 }$ cos θ = - $$\frac { 12 } { 13 }$$
Tan θ = $\frac { 5 } { 12 }$ 
B) sin θ = - $\frac { 5 } { 12 }$ cos θ = - $$\frac { 12 } { 13 }$$
Tan θ = - $\frac { 5 } { 13 }$ 
C) sin θ = - $\frac { 12 } { 13 }$ cos θ = - $\frac { 5 } { 13 }$
Tan θ = - $\frac { 5 } { 12 }$ 
D) sin θ = - $\frac { 5 } { 13 }$ cos θ = - $\frac { 5 } { 12 }$
Tan θ = - $\frac { 12 } { 13 }$ 
E) sin θ = - $\frac { 5 } { 13 }$ cos θ = - $\frac { 12 } { 13 }$
Tan θ = - $\frac { 5 } { 13 }$ 
A) sin θ = - $\frac { 5 } { 13 }$ cos θ = - $$\frac { 12 } { 13 }$$
Tan θ = $\frac { 5 } { 12 }$ 
B) sin θ = - $\frac { 5 } { 12 }$ cos θ = - $$\frac { 12 } { 13 }$$
Tan θ = - $\frac { 5 } { 13 }$ 
C) sin θ = - $\frac { 12 } { 13 }$ cos θ = - $\frac { 5 } { 13 }$
Tan θ = - $\frac { 5 } { 12 }$ 
D) sin θ = - $\frac { 5 } { 13 }$ cos θ = - $\frac { 5 } { 12 }$
Tan θ = - $\frac { 12 } { 13 }$ 
E) sin θ = - $\frac { 5 } { 13 }$ cos θ = - $\frac { 12 } { 13 }$
Tan θ = - $\frac { 5 } { 13 }$

Question 15

Use a calculator to evaluate cot 335 ${}^\circ$ .Round your answer to four decimal places. ​

Accepted Answer

A) -2.1445 
B) -2.6445 
C) -0.4470 
D) -1.1970 
E) -1.7453 
A) -2.1445 
B) -2.6445 
C) -0.4470 
D) -1.1970 
E) -1.7453

Question 16

Use a calculator to evaluate $\cot 3.3 ^ { \circ }$ .Round your answer to four decimal places.

Accepted Answer

A) 17.3432 
B) 17.8432 
C) 6.2599 
D) 13.8154 
E) 5.5099 
A) 17.3432 
B) 17.8432 
C) 6.2599 
D) 13.8154 
E) 5.5099

Question 17

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by​ $y = 2 e ^ { - t } \cos 6 t$ where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when $t = \frac { 1 } { 6 }$ .(Round your answer two decimal places. ) ​​   ​
​

Accepted Answer

A) 0.71 cm 
B) 1.11 cm 
C) 1.31 cm 
D) -0.91 cm 
E) 0.91 cm 
A) 0.71 cm 
B) 1.11 cm 
C) 1.31 cm 
D) -0.91 cm 
E) 0.91 cm

Question 18

Given the figure below,determine the value of $\sin \theta$ .​   ​

Accepted Answer

A) ​ $\sin \theta =$ $- \frac { 12 } { 13 }$ 
B)  $\sin \theta =$ $\frac { 12 } { 13 }$
​ 
C)  $\sin \theta =$ $\frac { 1 } { 2 }$ 
D)  $\sin \theta =$ $- \frac { 1 } { 2 }$ 
E)  $\sin \theta =$ $\frac { 3 } { 4 }$ 
A) ​ $\sin \theta =$ $- \frac { 12 } { 13 }$ 
B)  $\sin \theta =$ $\frac { 12 } { 13 }$
​ 
C)  $\sin \theta =$ $\frac { 1 } { 2 }$ 
D)  $\sin \theta =$ $- \frac { 1 } { 2 }$ 
E)  $\sin \theta =$ $\frac { 3 } { 4 }$

Question 19

State the quadrant in which θ lies if $\cos \theta$ > 0 and $\sin \theta$ > 0.

Accepted Answer

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

Question 20

Find the point (x,y)on the unit circle that corresponds to the real number $\frac { \pi } { 4 }$ .Use your results to evaluate tan t.

Accepted Answer

A)  $\tan t = - \frac { \sqrt { 3 } } { 2 }$ 
B)  $\tan t = 0$ 
C)  $\tan t = \frac { \sqrt { 3 } } { 2 }$ 
D)  $\tan t = 1$ 
E)  $\tan t = \text { undefmed }$ 
A)  $\tan t = - \frac { \sqrt { 3 } } { 2 }$ 
B)  $\tan t = 0$ 
C)  $\tan t = \frac { \sqrt { 3 } } { 2 }$ 
D)  $\tan t = 1$ 
E)  $\tan t = \text { undefmed }$

Exam 26: Trigonometric Functions of Any Angle

Determine the exact value of cot⁡θ\cot \thetacotθ when cos⁡θ=35\cos \theta = \frac { 3 } { 5 }cosθ=53​ and cot⁡θ>0\cot \theta > 0cotθ>0 .

The terminal side of θ lies on the line −15x−8y=0- 15 x - 8 y = 0−15x−8y=0 in the fourth quadrant.Find the exact value of cos⁡θ\cos \thetacosθ .

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Cot 171° ​

The point (7,24)is on the terminal side of an angle in standard position.Determine the exact value of cos θ.

Given the equation below,determine two solutions such that 0<θ<2π0 < \theta < 2 \pi0<θ<2π . sec​ θ = 233\frac { 2 \sqrt { 3 } } { 3 }323​​ ​

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. )​ cos⁡(−1180)\cos ( - 1180 )cos(−1180) ​

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) ​ Tan 306° ​

Find the reference angle θ′\theta^\primeθ′ ,and θ\thetaθ sketch and θ′\theta^\primeθ′ in standard position.​ θ=160∘\theta = 160 ^ { \circ }θ=160∘ ​

Determine the exact values of the three trigonometric functions csc,sec,and cot of the angle θ.​ ​ where a = 15 and b = 8. ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Tan ( -187°) ​

Evaluate the trigonometric function.Round your answer to four decimal places.​ csc⁡(−13π12)\csc \left( - \frac { 13 \pi } { 12 } \right)csc(−1213π​) ​

Determine the exact value of sin⁡(−225∘)\sin \left( - 225 ^ { \circ } \right)sin(−225∘) .

Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ.​ ​ where a=12 and b=5a = 12 \text { and } b = 5a=12 and b=5 ​

Use a calculator to evaluate cot 335 ∘{}^\circ∘ .Round your answer to four decimal places. ​

Use a calculator to evaluate cot⁡3.3∘\cot 3.3 ^ { \circ }cot3.3∘ .Round your answer to four decimal places.

Given the figure below,determine the value of sin⁡θ\sin \thetasinθ .​ ​

State the quadrant in which θ lies if cos⁡θ\cos \thetacosθ > 0 and sin⁡θ\sin \thetasinθ > 0.

Find the point (x,y)on the unit circle that corresponds to the real number π4\frac { \pi } { 4 }4π​ .Use your results to evaluate tan t.

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Determine the exact value of $\cot \theta$ when $\cos \theta = \frac { 3 } { 5 }$ and $\cot \theta > 0$ .

The terminal side of θ lies on the line $- 15 x - 8 y = 0$ in the fourth quadrant.Find the exact value of $\cos \theta$ .

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 171°

Given the equation below,determine two solutions such that $0 < \theta < 2 \pi$ . sec θ = $\frac { 2 \sqrt { 3 } } { 3 }$

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) $\cos ( - 1180 )$

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) Tan 306°

Find the reference angle $\theta^\prime$ ,and $\theta$ sketch and $\theta^\prime$ in standard position. $\theta = 160 ^ { \circ }$

Determine the exact values of the three trigonometric functions csc,sec,and cot of the angle θ. where a = 15 and b = 8.

Evaluate the trigonometric function.Round your answer to four decimal places. Tan ( -187°)

Evaluate the trigonometric function.Round your answer to four decimal places. $\csc \left( - \frac { 13 \pi } { 12 } \right)$

Determine the exact value of $\sin \left( - 225 ^ { \circ } \right)$ .

Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ. $Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ. where a = 12 \text { and } b = 5 $ where $a = 12 \text { and } b = 5$

Use a calculator to evaluate cot 335 ${}^\circ$ .Round your answer to four decimal places.

Use a calculator to evaluate $\cot 3.3 ^ { \circ }$ .Round your answer to four decimal places.

Given the figure below,determine the value of $\sin \theta$ . $Given the figure below,determine the value of \sin \theta . $

State the quadrant in which θ lies if $\cos \theta$ > 0 and $\sin \theta$ > 0.

Find the point (x,y)on the unit circle that corresponds to the real number $\frac { \pi } { 4 }$ .Use your results to evaluate tan t.