Question 1

Use the value of the trigonometric function to find $\csc t$ .​ $\sin ( - t ) = \frac { 3 } { 4 }$ ​

Accepted Answer

A)  $\csc t = \frac { 3 } { 4 }$ 
B)  $\csc t = - \frac { 3 } { 4 }$ 
C)  $\csc t = \infty$ 
D)  $\csc t = \frac { 4 } { 3 }$ 
E)  $\csc t = - \frac { 4 } { 3 }$ 
A)  $\csc t = \frac { 3 } { 4 }$ 
B)  $\csc t = - \frac { 3 } { 4 }$ 
C)  $\csc t = \infty$ 
D)  $\csc t = \frac { 4 } { 3 }$ 
E)  $\csc t = - \frac { 4 } { 3 }$

Question 2

Evaluate the trigonometric function using its period as an aid.​ $\sin 4 \pi$ ​

Accepted Answer

A)  $\sin 4 \pi = 4$ 
B)  $\sin 4 \pi = - 1$ 
C)  $\sin 4 \pi = - 4$ 
D)  $\sin 4 \pi = 0$ 
E)  $\sin 4 \pi = \infty$ 
A)  $\sin 4 \pi = 4$ 
B)  $\sin 4 \pi = - 1$ 
C)  $\sin 4 \pi = - 4$ 
D)  $\sin 4 \pi = 0$ 
E)  $\sin 4 \pi = \infty$

Question 3

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = \frac { 5 \pi } { 6 }$ ​

Accepted Answer

A)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . 
B)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
C)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
D)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
E)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
A)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . 
B)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ . 
C)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
D)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ . 
E)  $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ .

Question 4

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

Accepted Answer

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

Question 5

Evaluate the trigonometric function using its period as an aid.​ $\sin \left( \frac { 11 \pi } { 6 } \right)$ ​

Accepted Answer

A)  $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { 1 } { 2 }$ 
B)  $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { \sqrt { 2 } } { 2 }$ 
C)  $\sin \left( \frac { 11 \pi } { 6 } \right) = \infty$ 
D)  $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { 1 } { 2 }$ 
E)  $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { \sqrt { 2 } } { 2 }$ 
A)  $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { 1 } { 2 }$ 
B)  $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { \sqrt { 2 } } { 2 }$ 
C)  $\sin \left( \frac { 11 \pi } { 6 } \right) = \infty$ 
D)  $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { 1 } { 2 }$ 
E)  $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { \sqrt { 2 } } { 2 }$

Question 6

Use the value of the trigonometric function to find $\cos~ t$ .​ $\cos ( - t ) = - \frac { 1 } { 4 }$ ​

Accepted Answer

A)  $\cos t = \frac { 1 } { 4 }$ 
B)  $\cos t = - 4$ 
C)  $\cos t = \infty$ 
D)  $\cos t = 4$ 
E)  $\cos t = - \frac { 1 } { 4 }$ 
A)  $\cos t = \frac { 1 } { 4 }$ 
B)  $\cos t = - 4$ 
C)  $\cos t = \infty$ 
D)  $\cos t = 4$ 
E)  $\cos t = - \frac { 1 } { 4 }$

Question 7

Use the value of the trigonometric function to find $\sec ( - t )$ .​ $\cos t = - \frac { 3 } { 4 }$ ​

Accepted Answer

A)  $\sec ( - t ) = \frac { 4 } { 3 }$ 
B)  $\sec ( - t ) = - \frac { 3 } { 4 }$ 
C)  $\sec ( - t ) = - \frac { 4 } { 3 }$ 
D)  $\sec ( - t ) = \infty$ 
E)  $\sec ( - t ) = \frac { 3 } { 4 }$ 
A)  $\sec ( - t ) = \frac { 4 } { 3 }$ 
B)  $\sec ( - t ) = - \frac { 3 } { 4 }$ 
C)  $\sec ( - t ) = - \frac { 4 } { 3 }$ 
D)  $\sec ( - t ) = \infty$ 
E)  $\sec ( - t ) = \frac { 3 } { 4 }$

Question 8

Find the value of given trigonometric function.Round your answer to four decimal places..​ $$\csc \frac { 2 \pi } { 3 }$$ ​

Accepted Answer

A)  $\csc \frac { 2 \pi } { 3 } \approx 1.1547$ 
B)  $\csc \frac { 2 \pi } { 3 } \approx 1.2547$ 
C)  $\csc \frac { 2 \pi } { 3 } \approx - 1.1547$ 
D)  $\csc \frac { 2 \pi } { 3 } \approx 1.0547$ 
E)  $\csc \frac { 2 \pi } { 3 } \approx 1.3547$ 
A)  $\csc \frac { 2 \pi } { 3 } \approx 1.1547$ 
B)  $\csc \frac { 2 \pi } { 3 } \approx 1.2547$ 
C)  $\csc \frac { 2 \pi } { 3 } \approx - 1.1547$ 
D)  $\csc \frac { 2 \pi } { 3 } \approx 1.0547$ 
E)  $\csc \frac { 2 \pi } { 3 } \approx 1.3547$

Question 9

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​   ​ $$a = \frac { 4 } { 5 } , b = \frac { 3 } { 5 }$$ ​

Accepted Answer

A) ​ $\begin{array} { l } 
\sin t = - \frac { 3 } { 5 } \\
\cos t = - \frac { 4 } { 5 } \\
\tan t = - \frac { 3 } { 4 }
\end{array}$ ​ 
B) ​ $\begin{array} { l } 
\sin t = \frac { 3 } { 5 } \
\cos t = - \frac { 3 } { 4 } \
\tan t = \frac { 4 } { 5 }
\end{array}$ ​ 
C)  $\begin{array} { l } 
\sin t = - \frac { 3 } { 5 } \\
\cos t = - \frac { 3 } { 4 } \\
\tan t = \frac { 4 } { 5 }
\end{array}$ ​ 
D) ​ $\begin{array} { l } 
\sin t = \frac { 3 } { 4 } \\
\cos t = \frac { 3 } { 5 } \\
\tan t = \frac { 4 } { 5 }
\end{array}$ ​ 
E) ​ $\begin{array} { l } 
\sin t = - \frac { 3 } { 5 } \\
\cos t = - \frac { 4 } { 5 } \\
\tan t = \frac { 3 } { 4 }
\end{array}$ ​ 
A) ​ $\begin{array} { l } 
\sin t = - \frac { 3 } { 5 } \\
\cos t = - \frac { 4 } { 5 } \\
\tan t = - \frac { 3 } { 4 }
\end{array}$ ​ 
B) ​ $\begin{array} { l } 
\sin t = \frac { 3 } { 5 } \
\cos t = - \frac { 3 } { 4 } \
\tan t = \frac { 4 } { 5 }
\end{array}$ ​ 
C)  $\begin{array} { l } 
\sin t = - \frac { 3 } { 5 } \\
\cos t = - \frac { 3 } { 4 } \\
\tan t = \frac { 4 } { 5 }
\end{array}$ ​ 
D) ​ $\begin{array} { l } 
\sin t = \frac { 3 } { 4 } \\
\cos t = \frac { 3 } { 5 } \\
\tan t = \frac { 4 } { 5 }
\end{array}$ ​ 
E) ​ $\begin{array} { l } 
\sin t = - \frac { 3 } { 5 } \\
\cos t = - \frac { 4 } { 5 } \\
\tan t = \frac { 3 } { 4 }
\end{array}$ ​

Question 10

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = - \frac { 3 \pi } { 2 }$ ​

Accepted Answer

A)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\tan \left( - \frac { 3 \pi } { 2 } \right) = 0
\end{array}$ 
B)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 1 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\tan \left( - \frac { 3 \pi } { 2 } \right) = 0
\end{array}$ 
C)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $$( x , y ) = ( 0,1 )$$ . $$\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 1 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 0\\
\tan \left( - \frac { 3 \pi } { 2 } \right)~ is~ undefined.
\end{array}$$ 
D)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 1,0 )$ .​ $\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 1 \\
\tan \left( - \frac { 3 \pi } { 2 } \right) = 0
\end{array}$ ​ 
E) Not possible 
A)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\tan \left( - \frac { 3 \pi } { 2 } \right) = 0
\end{array}$ 
B)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 1 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\tan \left( - \frac { 3 \pi } { 2 } \right) = 0
\end{array}$ 
C)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $$( x , y ) = ( 0,1 )$$ . $$\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 1 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 0\\
\tan \left( - \frac { 3 \pi } { 2 } \right)~ is~ undefined.
\end{array}$$ 
D)  $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 1,0 )$ .​ $\begin{array} { l } 
\sin \left( - \frac { 3 \pi } { 2 } \right) = 0 \\
\cos \left( - \frac { 3 \pi } { 2 } \right) = 1 \\
\tan \left( - \frac { 3 \pi } { 2 } \right) = 0
\end{array}$ ​ 
E) Not possible

Question 11

Find the point $( x , y )$ on the unit circle that corresponds to the real number $\frac { 5 \pi } { 6 }$ .Use your results to evaluate $\cos t$ .

Accepted Answer

A)  $\cos t = \frac { \sqrt { 3 } } { 2 }$ 
B)  $\cos t = - \frac { \sqrt { 3 } } { 2 }$ 
C)  $\cos t = - \frac { 1 } { 2 }$ 
D)  $\cos t = - 1$ 
E)  $\cos t = 1$ 
A)  $\cos t = \frac { \sqrt { 3 } } { 2 }$ 
B)  $\cos t = - \frac { \sqrt { 3 } } { 2 }$ 
C)  $\cos t = - \frac { 1 } { 2 }$ 
D)  $\cos t = - 1$ 
E)  $\cos t = 1$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $t = 3 \pi$ corresponds to the point $( - 1,0 )$ . 
B)  $t = 3 \pi$ corresponds to the point $( 0 , - 1 )$ . 
C)  $t = 3 \pi$ corresponds to the point $( 0,3 )$ . 
D)  $t = 3 \pi$ corresponds to the point $( 3,0 )$ . 
E)  $t = 3 \pi$ corresponds to the point $( - 1 , - 1 )$ . 
A)  $t = 3 \pi$ corresponds to the point $( - 1,0 )$ . 
B)  $t = 3 \pi$ corresponds to the point $( 0 , - 1 )$ . 
C)  $t = 3 \pi$ corresponds to the point $( 0,3 )$ . 
D)  $t = 3 \pi$ corresponds to the point $( 3,0 )$ . 
E)  $t = 3 \pi$ corresponds to the point $( - 1 , - 1 )$ .

Question 14

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by $y ( t ) = \frac { 1 } { 4 } e ^ { - t } \cos 6 t$ ,where y is the displacement (in feet)and t is the time (in seconds).Complete the following table.(Round your answer to four decimal places. ) ​
$$\begin{array} { | c | c | c | c | c | c | } 
\hline\ t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & & & & & \
\hline
\end{array}$$

Accepted Answer

A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.1883 & 0.3614 & 0.0742 & - 0.1371 & 0.0883 \
\hline
\end{array}$$ 
E)  $\begin{array}{|l|l|l|l|l|l|}
\hline \t&1 & \frac{1}{8} & \frac{1}{5} & \frac{3}{7} & 5\\
\hline y & 0.0883 & 0.1614 & 0.0742 & 0.0629 & 0.2003\
\hline
\end{array}$ 
A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline \t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\
\hline y & 0.1883 & 0.3614 & 0.0742 & - 0.1371 & 0.0883 \
\hline
\end{array}$$ 
E)  $\begin{array}{|l|l|l|l|l|l|}
\hline \t&1 & \frac{1}{8} & \frac{1}{5} & \frac{3}{7} & 5\\
\hline y & 0.0883 & 0.1614 & 0.0742 & 0.0629 & 0.2003\
\hline
\end{array}$

Question 15

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\csc~ 0.5$ ​

Accepted Answer

A)  $\csc 0.5 \approx 2.2858$ 
B)  $\csc 0.5 \approx - 2.0858$ 
C)  $\csc 0.5 \approx 2.0858$ 
D)  $\csc 0.5 \approx 1.9858$ 
E)  $\csc~ 0.5 \approx 2.1858$ 
A)  $\csc 0.5 \approx 2.2858$ 
B)  $\csc 0.5 \approx - 2.0858$ 
C)  $\csc 0.5 \approx 2.0858$ 
D)  $\csc 0.5 \approx 1.9858$ 
E)  $\csc~ 0.5 \approx 2.1858$

Question 16

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

Accepted Answer

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

Question 17

Evaluate the trigonometric function using its period as an aid.​ $\sin \frac { 3 \pi } { 4 }$ ​

Accepted Answer

A)  $\sin \frac { 3 \pi } { 4 } = \infty$ 
B)  $\sin \frac { 3 \pi } { 4 } = - \sqrt { 2 }$ 
C)  $\sin \frac { 3 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$ 
D)  $\sin \frac { 3 \pi } { 4 } = \sqrt { 2 }$ 
E)  $\sin \frac { 3 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$ 
A)  $\sin \frac { 3 \pi } { 4 } = \infty$ 
B)  $\sin \frac { 3 \pi } { 4 } = - \sqrt { 2 }$ 
C)  $\sin \frac { 3 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$ 
D)  $\sin \frac { 3 \pi } { 4 } = \sqrt { 2 }$ 
E)  $\sin \frac { 3 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$

Question 18

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = \frac { 9 \pi } { 4 }$ ​

Accepted Answer

A)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = - 1
\end{array}$ 
B)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = 1
\end{array}$ ​ 
C)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = 1
\end{array}$ ​ 
D)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ .​ $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = - 1
\end{array}$ 
E) Not possible 
A)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = - 1
\end{array}$ 
B)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = 1
\end{array}$ ​ 
C)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = 1
\end{array}$ ​ 
D)  $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ .​ $\begin{array} { l } 
\sin \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \
\cos \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \
\tan \left( \frac { 9 \pi } { 4 } \right) = - 1
\end{array}$ 
E) Not possible

Question 19

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\sec ( - 22.3 )$ ​

Accepted Answer

A)  $\sec ( - 22.3 ) \approx - 0.8497$ 
B)  $\sec ( - 22.3 ) \approx 1.0497$ 
C)  $\sec ( - 22.3 ) \approx - 0.9497$ 
D)  $\sec ( - 22.3 ) \approx - 1.1497$ 
E)  $\sec ( - 22.3 ) \approx - 1.0497$ 
A)  $\sec ( - 22.3 ) \approx - 0.8497$ 
B)  $\sec ( - 22.3 ) \approx 1.0497$ 
C)  $\sec ( - 22.3 ) \approx - 0.9497$ 
D)  $\sec ( - 22.3 ) \approx - 1.1497$ 
E)  $\sec ( - 22.3 ) \approx - 1.0497$

Question 20

Find the point $( x , y )$ on the unit circle that corresponds to the real number $t = \frac { 5 \pi } { 4 }$ .Use your results to evaluate $\tan t$ .

Accepted Answer

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

Exam 24: Trigonometric Functions The Unit Circle

Use the value of the trigonometric function to find csc⁡t\csc tcsct .​ sin⁡(−t)=34\sin ( - t ) = \frac { 3 } { 4 }sin(−t)=43​ ​

Evaluate the trigonometric function using its period as an aid.​ sin⁡4π\sin 4 \pisin4π ​

Find the point (x,y)on the unit circle that corresponds to the real number t.​ t=5π6t = \frac { 5 \pi } { 6 }t=65π​ ​

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

Evaluate the trigonometric function using its period as an aid.​ sin⁡(11π6)\sin \left( \frac { 11 \pi } { 6 } \right)sin(611π​) ​

Use the value of the trigonometric function to find cos⁡ t\cos~ tcos t .​ cos⁡(−t)=−14\cos ( - t ) = - \frac { 1 } { 4 }cos(−t)=−41​ ​

Use the value of the trigonometric function to find sec⁡(−t)\sec ( - t )sec(−t) .​ cos⁡t=−34\cos t = - \frac { 3 } { 4 }cost=−43​ ​

Find the value of given trigonometric function.Round your answer to four decimal places..​ csc⁡2π3\csc \frac { 2 \pi } { 3 }csc32π​ ​

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​ ​ a=45,b=35a = \frac { 4 } { 5 } , b = \frac { 3 } { 5 }a=54​,b=53​ ​

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ t=−3π2t = - \frac { 3 \pi } { 2 }t=−23π​ ​

Find the point (x,y)( x , y )(x,y) on the unit circle that corresponds to the real number 5π6\frac { 5 \pi } { 6 }65π​ .Use your results to evaluate cos⁡t\cos tcost .

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

Find the point (x,y)on the unit circle that corresponds to the real number t.​ t=3πt = 3 \pit=3π ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ csc⁡ 0.5\csc~ 0.5csc 0.5 ​

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

Evaluate the trigonometric function using its period as an aid.​ sin⁡3π4\sin \frac { 3 \pi } { 4 }sin43π​ ​

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ t=9π4t = \frac { 9 \pi } { 4 }t=49π​ ​

Find the value of given trigonometric function.Round your answer to four decimal places.​ sec⁡(−22.3)\sec ( - 22.3 )sec(−22.3) ​

Find the point (x,y)( x , y )(x,y) on the unit circle that corresponds to the real number t=5π4t = \frac { 5 \pi } { 4 }t=45π​ .Use your results to evaluate tan⁡t\tan ttant .

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

Use the value of the trigonometric function to find $\csc t$ . $\sin ( - t ) = \frac { 3 } { 4 }$

Evaluate the trigonometric function using its period as an aid. $\sin 4 \pi$

Find the point (x,y)on the unit circle that corresponds to the real number t. $t = \frac { 5 \pi } { 6 }$

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

Evaluate the trigonometric function using its period as an aid. $\sin \left( \frac { 11 \pi } { 6 } \right)$

Use the value of the trigonometric function to find $\cos~ t$ . $\cos ( - t ) = - \frac { 1 } { 4 }$

Use the value of the trigonometric function to find $\sec ( - t )$ . $\cos t = - \frac { 3 } { 4 }$

Find the value of given trigonometric function.Round your answer to four decimal places.. $\csc \frac { 2 \pi } { 3 }$

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t. $Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t. a = \frac { 4 } { 5 } , b = \frac { 3 } { 5 } $ $a = \frac { 4 } { 5 } , b = \frac { 3 } { 5 }$

Evaluate (if possible)the sine,cosine,and tangent of the real number. $t = - \frac { 3 \pi } { 2 }$

Find the point $( x , y )$ on the unit circle that corresponds to the real number $\frac { 5 \pi } { 6 }$ .Use your results to evaluate $\cos t$ .

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

Find the value of given trigonometric function.Round your answer to four decimal places. $\csc~ 0.5$

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

Evaluate the trigonometric function using its period as an aid. $\sin \frac { 3 \pi } { 4 }$

Evaluate (if possible)the sine,cosine,and tangent of the real number. $t = \frac { 9 \pi } { 4 }$

Find the value of given trigonometric function.Round your answer to four decimal places. $\sec ( - 22.3 )$

Find the point $( x , y )$ on the unit circle that corresponds to the real number $t = \frac { 5 \pi } { 4 }$ .Use your results to evaluate $\tan t$ .