Question 1

Find the reference angle  θ′	heta ^ { \prime }θ′  ,and sketch  θ	hetaθ  and  θ′	heta ^ { \prime }θ′  in standard position.​  θ=8π7	heta = \frac { 8 \pi } { 7 }θ=78π​  ​

Accepted Answer

A)    θ′=π8	heta ^ { \prime } = \frac { \pi } { 8 }θ′=8π​  
B)    θ′=7π8	heta ^ { \prime } = \frac { 7 \pi } { 8 }θ′=87π​  
C)    θ′=8π	heta ^ { \prime } = 8 \piθ′=8π  
D)    θ′=π7	heta ^ { \prime } = \frac { \pi } { 7 }θ′=7π​  
E)    θ′=7π	heta ^ { \prime } = 7 \piθ′=7π

Question 2

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ.​  (5,12) ( 5,12 ) (5,12)   ​

Accepted Answer

A)  sin θ =  1213\frac { 12 } { 13 }1312​  cos θ =  513\frac { 5 } { 13 }135​ Tan θ =  125\frac { 12 } { 5 }512​ 
B)  sin θ =  1213\frac { 12 } { 13 }1312​  cos θ =  513\frac { 5 } { 13 }135​ Tan θ =  1213\frac { 12 } { 13 }1312​ 
C)  sin θ =  125\frac { 12 } { 5 }512​  cos θ =  513\frac { 5 } { 13 }135​ Tan θ =  1213\frac { 12 } { 13 }1312​ 
D)  sin θ =  513\frac { 5 } { 13 }135​  cos θ =  1213\frac { 12 } { 13 }1312​ Tan θ =  125\frac { 12 } { 5 }512​ 
E)  sin θ =  1213\frac { 12 } { 13 }1312​  cos θ =  125\frac { 12 } { 5 }512​ Tan θ =  513\frac { 5 } { 13 }135​

Question 3

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. )  ​
Tan 4.9
​

Accepted Answer

A)  -4.9675
B)  -4.8675
C)  -5.1675
D)  -4.7675
E)  -5.2675

Question 4

Evaluate the trigonometric function.Round your answer to four decimal places. ​
Cot 3.35
​

Accepted Answer

A)  7.7286
B)  5.7286
C)  5.2286
D)  6.7286
E)  4.7286

Question 5

The displacement from equilibrium of an oscillating weight suspended by a spring is given by​  y=2cos⁡6ty = 2 \cos 6 ty=2cos6t  ,where y is the displacement in centimeters and t is the time in seconds (see figure) .Find the displacement when  t=18t = \frac { 1 } { 8 }t=81​  .(Round your answers to two decimal places. ) ​  ​ ​

Accepted Answer

A)  1.76 cm
B)  1.66 cm
C)  1.46 cm
D)  1.86 cm
E)  1.96 cm

Question 6

The current I (in amperes) when 100 volts is applied to a circuit is given by​  I=5e−2tsin⁡tI = 5 e ^ { - 2 t } \sin tI=5e−2tsint  ​ where t is the time (in seconds) after the voltage is applied.Approximate the current at
T = 0.8 second after the voltage is applied.(Round your answers to two decimal places. ) 
​

Accepted Answer

A)  1.12 ampere
B)  1.02 ampere
C)  0.72 ampere
D)  0.82 ampere
E)  0.92 ampere

Question 7

Evaluate the trigonometric function.Round your answer to four decimal places.​  tan⁡(π3) 	an \left( \frac { \pi } { 3 } ight) tan(3π​)   ​

Accepted Answer

A)  2.2321
B)  1.7321
C)  2.7321
D)  3.7321
E)  4.7321

Question 8

Determine the exact value of  csc⁡θ\csc 	hetacscθ  when  cot⁡θ=2021\cot 	heta = \frac { 20 } { 21 }cotθ=2120​  and  csc⁡θ\csc 	hetacscθ  < 0.

Accepted Answer

A)    csc⁡θ=−1114\csc 	heta = - \frac { 11 } { 14 }cscθ=−1411​ 
B)    csc⁡θ=−32\csc 	heta = - \frac { 3 } { 2 }cscθ=−23​ 
C)    csc⁡θ=−5821\csc 	heta = - \frac { 58 } { 21 }cscθ=−2158​ 
D)    csc⁡θ=−821\csc 	heta = - \frac { 8 } { 21 }cscθ=−218​ 
E)    csc⁡θ=−2921\csc 	heta = - \frac { 29 } { 21 }cscθ=−2129​

Question 9

Evaluate the trigonometric function.Round your answer to four decimal places.​  cot⁡(−13π5) \cot \left( - \frac { 13 \pi } { 5 } \right) cot(−513π​)   ​

Accepted Answer

A)  0.8249
B)  3.3249
C)  0.3249
D)  2.3249
E)  1.3249

Question 10

The displacement from equilibrium of an oscillating weight suspended by a spring is given by​  y=2cos⁡6ty = 2 \cos 6 ty=2cos6t  ​ where y is the displacement in centimeters and t is the time in seconds (see figure) .Find the displacement when  t=7t = 7t=7  .(Round your answers to nearest tenth. ) ​  ​

Accepted Answer

A)  1.200 cm
B)  1.100 cm
C)  1.000 cm
D)  0.800 cm
E)  1.300 cm

Question 11

Evaluate the trigonometric function.Round your answer to four decimal places.​  tan⁡(−π8) 	an \left( - \frac { \pi } { 8 } ight) tan(−8π​)   ​

Accepted Answer

A)  0.5858
B)  -0.4142
C)  0.0858
D)  2.5858
E)  1.5858

Question 12

Given the equation below,determine two solutions such that  0∘<θ<360∘0 ^ { \circ } < 	heta < 360 ^ { \circ }0∘<θ<360∘  . ​cos θ =  −32- \frac { \sqrt { 3 } } { 2 }−23​​

Accepted Answer

A)  ​θ = 225  ∘{}^\circ∘  ,135  ∘{}^\circ∘ 
B)  θ = 135  ∘{}^\circ∘  ,225  ∘{}^\circ∘ 
C)  θ = 150  ∘{}^\circ∘  ,210  ∘{}^\circ∘ 
D)  θ = 300  ∘{}^\circ∘  ,240  ∘{}^\circ∘ 
E)  θ = 30  ∘{}^\circ∘

Question 13

Use a calculator to evaluate  sin⁡5∘\sin 5 ^ { \circ }sin5∘  .Round your answer to four decimal places.

Accepted Answer

A)  -0.9589
B)  0.0872
C)  -0.4128
D)  -0.4282
E)  -1.7089

Exam 26: Trigonometric Functions of Any Angle

Given the equation below,determine two solutions such that $0 ^ { \circ } < \theta < 360 ^ { \circ }$ . cos θ = $- \frac { \sqrt { 3 } } { 2 }$

Correct Answer
verified

Determine the exact value of $\csc \theta$ when $\cot \theta = \frac { 20 } { 21 }$ and $\csc \theta$ < 0.

Correct Answer
verified

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. $\tan \left( \frac { \pi } { 3 } \right)$

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) Tan 4.9

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. $\cot \left( - \frac { 13 \pi } { 5 } \right)$

Correct Answer
verified

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. $\tan \left( - \frac { \pi } { 8 } \right)$

Correct Answer
verified

The current I (in amperes) when 100 volts is applied to a circuit is given by $I = 5 e ^ { - 2 t } \sin t$ where t is the time (in seconds) after the voltage is applied.Approximate the current at T = 0.8 second after the voltage is applied.(Round your answers to two decimal places. )

Correct Answer
verified

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ. $( 5,12 )$

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 3.35

Correct Answer
verified

Use a calculator to evaluate $\sin 5 ^ { \circ }$ .Round your answer to four decimal places.

Correct Answer
verified

Find the reference angle $\theta ^ { \prime }$ ,and sketch $\theta$ and $\theta ^ { \prime }$ in standard position. $\theta = \frac { 8 \pi } { 7 }$

Correct Answer
verified

Exam 26: Trigonometric Functions of Any Angle

Given the equation below,determine two solutions such that 0∘<θ<360∘0 ^ { \circ } < \theta < 360 ^ { \circ }0∘<θ<360∘ . ​cos θ = −32- \frac { \sqrt { 3 } } { 2 }−23​​

Correct AnswerverifiedShow Answer

Determine the exact value of csc⁡θ\csc \thetacscθ when cot⁡θ=2021\cot \theta = \frac { 20 } { 21 }cotθ=2120​ and csc⁡θ\csc \thetacscθ < 0.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Evaluate the trigonometric function.Round your answer to four decimal places.​ tan⁡(π3) \tan \left( \frac { \pi } { 3 } \right) tan(3π​) ​

Correct AnswerverifiedShow Answer

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) ​ Tan 4.9 ​

Correct AnswerverifiedShow Answer

Evaluate the trigonometric function.Round your answer to four decimal places.​ cot⁡(−13π5) \cot \left( - \frac { 13 \pi } { 5 } \right) cot(−513π​) ​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Evaluate the trigonometric function.Round your answer to four decimal places.​ tan⁡(−π8) \tan \left( - \frac { \pi } { 8 } \right) tan(−8π​) ​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ.​ (5,12) ( 5,12 ) (5,12) ​

Correct AnswerverifiedShow Answer

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Cot 3.35 ​

Correct AnswerverifiedShow Answer

Use a calculator to evaluate sin⁡5∘\sin 5 ^ { \circ }sin5∘ .Round your answer to four decimal places.

Correct AnswerverifiedShow Answer

Find the reference angle θ′\theta ^ { \prime }θ′ ,and sketch θ\thetaθ and θ′\theta ^ { \prime }θ′ in standard position.​ θ=8π7\theta = \frac { 8 \pi } { 7 }θ=78π​ ​

Correct AnswerverifiedShow Answer

Given the equation below,determine two solutions such that $0 ^ { \circ } < \theta < 360 ^ { \circ }$ . cos θ = $- \frac { \sqrt { 3 } } { 2 }$

Correct Answer
verified

Determine the exact value of $\csc \theta$ when $\cot \theta = \frac { 20 } { 21 }$ and $\csc \theta$ < 0.

Correct Answer
verified

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. $\tan \left( \frac { \pi } { 3 } \right)$

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) Tan 4.9

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. $\cot \left( - \frac { 13 \pi } { 5 } \right)$

Correct Answer
verified

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. $\tan \left( - \frac { \pi } { 8 } \right)$

Correct Answer
verified

Correct Answer
verified

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ. $( 5,12 )$

Correct Answer
verified

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 3.35

Correct Answer
verified

Use a calculator to evaluate $\sin 5 ^ { \circ }$ .Round your answer to four decimal places.

Correct Answer
verified

Find the reference angle $\theta ^ { \prime }$ ,and sketch $\theta$ and $\theta ^ { \prime }$ in standard position. $\theta = \frac { 8 \pi } { 7 }$

Correct Answer
verified