Question 1

Evaluate (if possible)the sine,cosec,and tangent of the real number.​ $t = - 8 \pi$ ​

Accepted Answer

A)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) \text { is undefined } \
\tan ( - 8 \pi ) = 0
\end{array}$ 
B)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$ 
C)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$ 
D)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$ 
E) Not possible 
A)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) \text { is undefined } \
\tan ( - 8 \pi ) = 0
\end{array}$ 
B)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 0 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$ 
C)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$ 
D)  $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } 
\sin ( - 8 \pi ) = 1 \
\csc ( - 8 \pi ) = 0 \
\tan ( - 8 \pi ) \text { is undefined }
\end{array}$ 
E) Not possible A

Question 2

Use the value of the trigonometric function to find $\cos ( \pi - t )$ .​ $\cos t = \frac { 5 } { 6 }$ ​

Accepted Answer

A)  $\cos ( \pi - t ) = \frac { 5 } { 6 }$ 
B)  $\cos ( \pi - t ) = - \frac { 5 } { 6 }$ 
C)  $\cos ( \pi - t ) = \frac { 6 } { 5 }$ 
D)  $\cos ( \pi - t ) = \infty$ 
E)  $\cos ( \pi - t ) = - \frac { 6 } { 5 }$ 
A)  $\cos ( \pi - t ) = \frac { 5 } { 6 }$ 
B)  $\cos ( \pi - t ) = - \frac { 5 } { 6 }$ 
C)  $\cos ( \pi - t ) = \frac { 6 } { 5 }$ 
D)  $\cos ( \pi - t ) = \infty$ 
E)  $\cos ( \pi - t ) = - \frac { 6 } { 5 }$ B

Question 3

Use the value of the trigonometric function to find the $\sin ( - t )$ .​ $\sin t = \frac { 1 } { 6 }$ ​

Accepted Answer

A)  $\sin ( - t ) = - \frac { 1 } { 6 }$ 
B)  $\sin ( - t ) = - 6$ 
C)  $\sin ( - t ) = 6$ 
D)  $\sin ( - t ) = \infty$ 
E)  $\sin ( - t ) = \frac { 1 } { 6 }$ 
A)  $\sin ( - t ) = - \frac { 1 } { 6 }$ 
B)  $\sin ( - t ) = - 6$ 
C)  $\sin ( - t ) = 6$ 
D)  $\sin ( - t ) = \infty$ 
E)  $\sin ( - t ) = \frac { 1 } { 6 }$ A

Question 4

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cot ( - 0.9 )$ ​

Accepted Answer

A)  $\cot ( - 0.9 ) \approx - 0.6936$ 
B)  $\cot ( - 0.9 ) \approx - 0.7936$ 
C)  $\cot ( - 0.9 ) \approx - 0.5936$ 
D)  $\cot ( - 0.9 ) \approx - 0.8936$ 
E)  $\cot ( - 0.9 ) \approx 0.7936$ 
A)  $\cot ( - 0.9 ) \approx - 0.6936$ 
B)  $\cot ( - 0.9 ) \approx - 0.7936$ 
C)  $\cot ( - 0.9 ) \approx - 0.5936$ 
D)  $\cot ( - 0.9 ) \approx - 0.8936$ 
E)  $\cot ( - 0.9 ) \approx 0.7936$

Question 5

Use the value of the trigonometric function to find $\csc ( - t )$ .​ $\sin t = \frac { 1 } { 6 }$ ​

Accepted Answer

A)  $\csc ( - t ) = \frac { 1 } { 6 }$ 
B)  $\csc ( - t ) = 6$ 
C)  $\csc ( - t ) = - \frac { 1 } { 6 }$ 
D)  $\csc ( - t ) = - 6$ 
E)  $\csc ( - t ) = \infty$ 
A)  $\csc ( - t ) = \frac { 1 } { 6 }$ 
B)  $\csc ( - t ) = 6$ 
C)  $\csc ( - t ) = - \frac { 1 } { 6 }$ 
D)  $\csc ( - t ) = - 6$ 
E)  $\csc ( - t ) = \infty$

Question 6

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​   ​ $a = \frac { 12 } { 13 } , b = \frac { 5 } { 13 }$ ​

Accepted Answer

A) ​ $\begin{array} { l } 
\sin t = - \frac { 5 } { 13 } \\
\cos t = - \frac { 12 } { 13 } \\
\tan t = - \frac { 5 } { 12 }
\end{array}$ ​ 
B) ​ $\begin{array} { l } 
\sin t = \frac { 5 } { 13 } \\
\cos t = \frac { 12 } { 13 } \\
\tan t = \frac { 5 } { 12 }
\end{array}$ ​ 
C)  $\begin{array} { l } 
\sin t = \frac { 5 } { 13 } \\\
\cos t = - \frac { 12 } { 13 } \\
\tan t = - \frac { 5 } { 12 }
\end{array}$ ​ 
D) ​ $\begin{array} { l } 
\sin t = \frac { 5 } { 12 } \\
\cos t = \frac { 5 } { 13 } \\
\tan t = \frac { 12 } { 13 }
\end{array}$ ​ 
E) ​ $\begin{array} { l } 
\sin t = \frac { 5 } { 13 } \
\cos t = - \frac { 12 } { 13 } \
\tan t = \frac { 5 } { 12 }
\end{array}$ ​ 
A) ​ $\begin{array} { l } 
\sin t = - \frac { 5 } { 13 } \\
\cos t = - \frac { 12 } { 13 } \\
\tan t = - \frac { 5 } { 12 }
\end{array}$ ​ 
B) ​ $\begin{array} { l } 
\sin t = \frac { 5 } { 13 } \\
\cos t = \frac { 12 } { 13 } \\
\tan t = \frac { 5 } { 12 }
\end{array}$ ​ 
C)  $\begin{array} { l } 
\sin t = \frac { 5 } { 13 } \\\
\cos t = - \frac { 12 } { 13 } \\
\tan t = - \frac { 5 } { 12 }
\end{array}$ ​ 
D) ​ $\begin{array} { l } 
\sin t = \frac { 5 } { 12 } \\
\cos t = \frac { 5 } { 13 } \\
\tan t = \frac { 12 } { 13 }
\end{array}$ ​ 
E) ​ $\begin{array} { l } 
\sin t = \frac { 5 } { 13 } \
\cos t = - \frac { 12 } { 13 } \
\tan t = \frac { 5 } { 12 }
\end{array}$ ​

Question 7

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = \frac { 10 \pi } { 3 }$ ​

Accepted Answer

A)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
B)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . 
C)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
D)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $$\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$$ . 
E)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . 
A)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
B)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . 
C)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
D)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $$\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$$ . 
E)  $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ .

Question 8

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cot \frac { \pi } { 7 }$ ​

Accepted Answer

A)  $\cot \frac { \pi } { 7 } \approx 2.0765$ 
B)  $\cot \frac { \pi } { 7 } \approx 1.9765$ 
C)  $\cot \frac { \pi } { 7 } \approx 2.2765$ 
D)  $\cot \frac { \pi } { 7 } \approx - 2.0765$ 
E)  $\cot \frac { \pi } { 7 } \approx 2.1765$ 
A)  $\cot \frac { \pi } { 7 } \approx 2.0765$ 
B)  $\cot \frac { \pi } { 7 } \approx 1.9765$ 
C)  $\cot \frac { \pi } { 7 } \approx 2.2765$ 
D)  $\cot \frac { \pi } { 7 } \approx - 2.0765$ 
E)  $\cot \frac { \pi } { 7 } \approx 2.1765$

Question 9

Evaluate the trigonometric function using its period as an aid.​ $\cos \frac { 5 \pi } { 3 }$ ​

Accepted Answer

A)  $\cos \frac { 5 \pi } { 3 } = \infty$ 
B)  $\cos \frac { 5 \pi } { 3 } = - \frac { 1 } { 2 }$ 
C)  $\cos \frac { 5 \pi } { 3 } = 2$ 
D)  $\cos \frac { 5 \pi } { 3 } = - 2$ 
E)  $\cos \frac { 5 \pi } { 3 } = \frac { 1 } { 2 }$ 
A)  $\cos \frac { 5 \pi } { 3 } = \infty$ 
B)  $\cos \frac { 5 \pi } { 3 } = - \frac { 1 } { 2 }$ 
C)  $\cos \frac { 5 \pi } { 3 } = 2$ 
D)  $\cos \frac { 5 \pi } { 3 } = - 2$ 
E)  $\cos \frac { 5 \pi } { 3 } = \frac { 1 } { 2 }$

Question 10

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\tan \frac { \pi } { 8 }$ ​

Accepted Answer

A)  $\tan \frac { \pi } { 8 } \approx$ 0.3142 
B)  $\tan \frac { \pi } { 8 } \approx$ 0.6142 
C)  $\tan \frac { \pi } { 8 } \approx$ - 0.4142 
D)  $\tan \frac { \pi } { 8 } \approx$ 0.4142 
E)  $\tan \frac { \pi } { 8 } \approx$ 0.5142 
A)  $\tan \frac { \pi } { 8 } \approx$ 0.3142 
B)  $\tan \frac { \pi } { 8 } \approx$ 0.6142 
C)  $\tan \frac { \pi } { 8 } \approx$ - 0.4142 
D)  $\tan \frac { \pi } { 8 } \approx$ 0.4142 
E)  $\tan \frac { \pi } { 8 } \approx$ 0.5142

Question 11

Use the value of the trigonometric function to find $\sin ( t + \pi )$ .​ $\sin t = \frac { 7 } { 8 }$ ​

Accepted Answer

A)  $\sin ( t + \pi ) = - \frac { 8 } { 7 }$ 
B)  $\sin ( t + \pi ) = \frac { 8 } { 7 }$ 
C)  $\sin ( t + \pi ) = \frac { 7 } { 8 }$ 
D)  $\sin ( t + \pi ) = \infty$ 
E)  $\sin ( t + \pi ) = - \frac { 7 } { 8 }$ 
A)  $\sin ( t + \pi ) = - \frac { 8 } { 7 }$ 
B)  $\sin ( t + \pi ) = \frac { 8 } { 7 }$ 
C)  $\sin ( t + \pi ) = \frac { 7 } { 8 }$ 
D)  $\sin ( t + \pi ) = \infty$ 
E)  $\sin ( t + \pi ) = - \frac { 7 } { 8 }$

Question 12

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\text { sec } 1.6$ ​

Accepted Answer

A)  $\sec 1.6 \approx - 34.1471$ 
B)  $\sec 1.6 \approx - 34.0471$ 
C)  $\sec 1.6 \approx - 34.2471$ 
D)  $\sec 1.6 \approx - 34.3471$ 
E)  $\sec 1.6 \approx 34.2471$ 
A)  $\sec 1.6 \approx - 34.1471$ 
B)  $\sec 1.6 \approx - 34.0471$ 
C)  $\sec 1.6 \approx - 34.2471$ 
D)  $\sec 1.6 \approx - 34.3471$ 
E)  $\sec 1.6 \approx 34.2471$

Question 13

Use the value of the trigonometric function to find $\sin ( \pi - t )$ .​ $\sin t = \frac { 6 } { 7 }$ ​

Accepted Answer

A)  $\sin ( \pi - t ) = \frac { 6 } { 7 }$ 
B)  $\sin ( \pi - t ) = - \frac { 6 } { 7 }$ 
C)  $\sin ( \pi - t ) = - \frac { 7 } { 6 }$ 
D)  $\sin ( \pi - t ) = \infty$ 
E)  $\sin ( \pi - t ) = \frac { 7 } { 6 }$ 
A)  $\sin ( \pi - t ) = \frac { 6 } { 7 }$ 
B)  $\sin ( \pi - t ) = - \frac { 6 } { 7 }$ 
C)  $\sin ( \pi - t ) = - \frac { 7 } { 6 }$ 
D)  $\sin ( \pi - t ) = \infty$ 
E)  $\sin ( \pi - t ) = \frac { 7 } { 6 }$

Question 14

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = 3 \cos 10 t$ ,where y is the displacement in centimeters and t is the time in seconds.Find the displacement when $t = 0.65$ ,rounding answer to four decimal places.

Accepted Answer

A) -3.7018 cm 
B) -6.4350 cm 
C) 23.8825 cm 
D) 2.9298 cm 
E) -1.6362 cm 
A) -3.7018 cm 
B) -6.4350 cm 
C) 23.8825 cm 
D) 2.9298 cm 
E) -1.6362 cm

Question 15

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos 6 t$ ,where y is the displacement (in feet)and t is the time (in seconds).Find the displacements when $t = \frac { 1 } { 2 }$ .
​

Accepted Answer

A)  $y \left( \frac { 1 } { 2 } \right) \approx - 0.15$ foot 
B)  $y \left( \frac { 1 } { 2 } \right) \approx 0.15$ foot 
C)  $y \left( \frac { 1 } { 2 } \right) \approx - 0.05$ foot 
D)  $y \left( \frac { 1 } { 2 } \right) \approx 0.05$ foot 
E)  $y \left( \frac { 1 } { 2 } \right) \approx - 0.25$ foot 
A)  $y \left( \frac { 1 } { 2 } \right) \approx - 0.15$ foot 
B)  $y \left( \frac { 1 } { 2 } \right) \approx 0.15$ foot 
C)  $y \left( \frac { 1 } { 2 } \right) \approx - 0.05$ foot 
D)  $y \left( \frac { 1 } { 2 } \right) \approx 0.05$ foot 
E)  $y \left( \frac { 1 } { 2 } \right) \approx - 0.25$ foot

Question 16

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = - \frac { \pi } { 2 }$ ​

Accepted Answer

A)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = 0 \
\cos \left( - \frac { \pi } { 2 } \right) = 0 \
\tan \left( - \frac { \pi } { 2 } \right) = 0
\end{array}$ 
B)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = - 1 \
\cos \left( - \frac { \pi } { 2 } \right) = 0 \
\tan \left( - \frac { \pi } { 2 } \right) = 0
\end{array}$ 
C)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = - 1 \
\cos \left( - \frac { \pi } { 2 } \right) = 0 \
\tan \left( - \frac { \pi } { 2 } \right) \text { is undefined }
\end{array}$ 
D)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = 0 \
\cos \left( - \frac { \pi } { 2 } \right) = - 1 \
\tan \left( - \frac { \pi } { 2 } \right) = 0
\end{array}$ 
E) Not possible 
A)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = 0 \
\cos \left( - \frac { \pi } { 2 } \right) = 0 \
\tan \left( - \frac { \pi } { 2 } \right) = 0
\end{array}$ 
B)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = - 1 \
\cos \left( - \frac { \pi } { 2 } \right) = 0 \
\tan \left( - \frac { \pi } { 2 } \right) = 0
\end{array}$ 
C)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = - 1 \
\cos \left( - \frac { \pi } { 2 } \right) = 0 \
\tan \left( - \frac { \pi } { 2 } \right) \text { is undefined }
\end{array}$ 
D)  $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { \pi } { 2 } \right) = 0 \
\cos \left( - \frac { \pi } { 2 } \right) = - 1 \
\tan \left( - \frac { \pi } { 2 } \right) = 0
\end{array}$ 
E) Not possible

Question 17

Use the value of the trigonometric function to find $\cos ( - t )$ .​ $\cos t = - \frac { 3 } { 8 }$ ​

Accepted Answer

A)  $\cos ( - t ) = \frac { 8 } { 3 }$ 
B)  $\cos ( - t ) = \frac { 3 } { 8 }$ 
C)  $\cos ( - t ) = - \frac { 3 } { 8 }$ 
D)  $\cos ( - t ) = - \frac { 8 } { 3 }$ 
E)  $\cos ( - t ) = \infty$ 
A)  $\cos ( - t ) = \frac { 8 } { 3 }$ 
B)  $\cos ( - t ) = \frac { 3 } { 8 }$ 
C)  $\cos ( - t ) = - \frac { 3 } { 8 }$ 
D)  $\cos ( - t ) = - \frac { 8 } { 3 }$ 
E)  $\cos ( - t ) = \infty$

Question 18

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = \frac { 25 \pi } { 3 }$ ​

Accepted Answer

A)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = - \sqrt { 3 }
\end{array}$ 
B)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { 1 } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = \sqrt { 3 }
\end{array}$ 
C)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\
\cos \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 2 } \\
\tan \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
D)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \\
\tan \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
E) Not possible 
A)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = - \sqrt { 3 }
\end{array}$ 
B)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { 1 } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = \sqrt { 3 }
\end{array}$ 
C)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\
\cos \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 2 } \\
\tan \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
D)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \\
\tan \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
E) Not possible

Question 19

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cos ( - 1.6 )$ ​

Accepted Answer

A)  $\cos ( - 1.6 ) \approx 0.1708$ 
B)  $\cos ( - 1.6 ) \approx 0.0708$ 
C)  $\cos ( - 1.6 ) \approx 0.0292$ 
D)  $\cos ( - 1.6 ) \approx - 0.0292$ 
E)  $\cos ( - 1.6 ) \approx - 0.1292$ 
A)  $\cos ( - 1.6 ) \approx 0.1708$ 
B)  $\cos ( - 1.6 ) \approx 0.0708$ 
C)  $\cos ( - 1.6 ) \approx 0.0292$ 
D)  $\cos ( - 1.6 ) \approx - 0.0292$ 
E)  $\cos ( - 1.6 ) \approx - 0.1292$

Question 20

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = \frac { 19 \pi } { 3 }$ ​

Accepted Answer

A)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
B)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
C)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . 
D)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . 
E)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
A)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
B)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
C)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . 
D)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . 
E)  $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ .

Exam 24: Trigonometric Functions The Unit Circle

Evaluate (if possible)the sine,cosec,and tangent of the real number.​ t=−8πt = - 8 \pit=−8π ​

Use the value of the trigonometric function to find cos⁡(π−t)\cos ( \pi - t )cos(π−t) .​ cos⁡t=56\cos t = \frac { 5 } { 6 }cost=65​ ​

Use the value of the trigonometric function to find the sin⁡(−t)\sin ( - t )sin(−t) .​ sin⁡t=16\sin t = \frac { 1 } { 6 }sint=61​ ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ cot⁡(−0.9)\cot ( - 0.9 )cot(−0.9) ​

Use the value of the trigonometric function to find csc⁡(−t)\csc ( - t )csc(−t) .​ sin⁡t=16\sin t = \frac { 1 } { 6 }sint=61​ ​

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​ ​ a=1213,b=513a = \frac { 12 } { 13 } , b = \frac { 5 } { 13 }a=1312​,b=135​ ​

Find the point (x,y)on the unit circle that corresponds to the real number t.​ t=10π3t = \frac { 10 \pi } { 3 }t=310π​ ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ cot⁡π7\cot \frac { \pi } { 7 }cot7π​ ​

Evaluate the trigonometric function using its period as an aid.​ cos⁡5π3\cos \frac { 5 \pi } { 3 }cos35π​ ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ tan⁡π8\tan \frac { \pi } { 8 }tan8π​ ​

Use the value of the trigonometric function to find sin⁡(t+π)\sin ( t + \pi )sin(t+π) .​ sin⁡t=78\sin t = \frac { 7 } { 8 }sint=87​ ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ sec 1.6\text { sec } 1.6 sec 1.6 ​

Use the value of the trigonometric function to find sin⁡(π−t)\sin ( \pi - t )sin(π−t) .​ sin⁡t=67\sin t = \frac { 6 } { 7 }sint=76​ ​

The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t)=14cos⁡6ty ( t ) = \frac { 1 } { 4 } \cos 6 ty(t)=41​cos6t ,where y is the displacement (in feet)and t is the time (in seconds).Find the displacements when t=12t = \frac { 1 } { 2 }t=21​ . ​

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ t=−π2t = - \frac { \pi } { 2 }t=−2π​ ​

Use the value of the trigonometric function to find cos⁡(−t)\cos ( - t )cos(−t) .​ cos⁡t=−38\cos t = - \frac { 3 } { 8 }cost=−83​ ​

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ t=25π3t = \frac { 25 \pi } { 3 }t=325π​ ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ cos⁡(−1.6)\cos ( - 1.6 )cos(−1.6) ​

Find the point (x,y)on the unit circle that corresponds to the real number t.​ t=19π3t = \frac { 19 \pi } { 3 }t=319π​ ​

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

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

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

Evaluate (if possible)the sine,cosec,and tangent of the real number. $t = - 8 \pi$

Use the value of the trigonometric function to find $\cos ( \pi - t )$ . $\cos t = \frac { 5 } { 6 }$

Use the value of the trigonometric function to find the $\sin ( - t )$ . $\sin t = \frac { 1 } { 6 }$

Find the value of given trigonometric function.Round your answer to four decimal places. $\cot ( - 0.9 )$

Use the value of the trigonometric function to find $\csc ( - t )$ . $\sin t = \frac { 1 } { 6 }$

Find the point (x,y)on the unit circle that corresponds to the real number t. $t = \frac { 10 \pi } { 3 }$

Find the value of given trigonometric function.Round your answer to four decimal places. $\cot \frac { \pi } { 7 }$

Evaluate the trigonometric function using its period as an aid. $\cos \frac { 5 \pi } { 3 }$

Find the value of given trigonometric function.Round your answer to four decimal places. $\tan \frac { \pi } { 8 }$

Use the value of the trigonometric function to find $\sin ( t + \pi )$ . $\sin t = \frac { 7 } { 8 }$

Find the value of given trigonometric function.Round your answer to four decimal places. $\text { sec } 1.6$

Use the value of the trigonometric function to find $\sin ( \pi - t )$ . $\sin t = \frac { 6 } { 7 }$

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos 6 t$ ,where y is the displacement (in feet)and t is the time (in seconds).Find the displacements when $t = \frac { 1 } { 2 }$ .

Evaluate (if possible)the sine,cosine,and tangent of the real number. $t = - \frac { \pi } { 2 }$

Use the value of the trigonometric function to find $\cos ( - t )$ . $\cos t = - \frac { 3 } { 8 }$

Evaluate (if possible)the sine,cosine,and tangent of the real number. $t = \frac { 25 \pi } { 3 }$

Find the value of given trigonometric function.Round your answer to four decimal places. $\cos ( - 1.6 )$

Find the point (x,y)on the unit circle that corresponds to the real number t. $t = \frac { 19 \pi } { 3 }$