Question 1

Find to two decimal places the approximate value of $\tan ( 1.5 )$

Accepted Answer

The answer of Find to two decimal places the approximate...

Question 2

Suppose that point $P \left( \frac { \sqrt { 5 } } { 5 } , - \frac { 2 \sqrt { 5 } } { 5 } \right)$ is on the unit circle. Find $\sin t$ and $\cos t$

Accepted Answer

A)  $\sin t = - \frac { 2 \sqrt { 5 } } { 5 } , \quad \cos t = \frac { \sqrt { 5 } } { 5 }$ 
B)  $\sin t = - \frac { \sqrt { 5 } } { 5 } , \quad \cos t = \frac { \sqrt { 5 } } { 5 }$ 
C)  $\sin t = \frac { \sqrt { 5 } } { 5 } , \quad \cos t = - \frac { 2 \sqrt { 5 } } { 5 }$ 
D)  $\sin t = 2 \sqrt { 5 } , \cos t = \frac { \sqrt { 5 } } { 5 }$ 
E)  none of these 
A)  $\sin t = - \frac { 2 \sqrt { 5 } } { 5 } , \quad \cos t = \frac { \sqrt { 5 } } { 5 }$ 
B)  $\sin t = - \frac { \sqrt { 5 } } { 5 } , \quad \cos t = \frac { \sqrt { 5 } } { 5 }$ 
C)  $\sin t = \frac { \sqrt { 5 } } { 5 } , \quad \cos t = - \frac { 2 \sqrt { 5 } } { 5 }$ 
D)  $\sin t = 2 \sqrt { 5 } , \cos t = \frac { \sqrt { 5 } } { 5 }$ 
E)  none of these

Question 3

Find the period and the shift for the function $y = 2 \cot \left( 3 x - \frac { \pi } { 2 } \right)$

Accepted Answer

A)  $\text { period: } \frac { \pi } { 3 } \text {, shift: } \frac { \pi } { 6 } \text { to the right }$ 
B)  $\text { period: } \frac { 2 \pi } { 3 } \text {, shift: } \frac { \pi } { 6 } \text { to the right }$ 
C)  $\text { period: } \frac { \pi } { 3 } \text {, shitt: } \frac { \pi } { 2 } \text { to the left }$ 
D)  $\text { period: } 3 \pi \text {, shift: } \frac { 3 \pi } { 2 } \text { to the right }$ 
E)  $\text { period: } \frac { \pi } { 3 } \text {, shitt: } \frac { \pi } { 6 } \text { to the left }$ 
A)  $\text { period: } \frac { \pi } { 3 } \text {, shift: } \frac { \pi } { 6 } \text { to the right }$ 
B)  $\text { period: } \frac { 2 \pi } { 3 } \text {, shift: } \frac { \pi } { 6 } \text { to the right }$ 
C)  $\text { period: } \frac { \pi } { 3 } \text {, shitt: } \frac { \pi } { 2 } \text { to the left }$ 
D)  $\text { period: } 3 \pi \text {, shift: } \frac { 3 \pi } { 2 } \text { to the right }$ 
E)  $\text { period: } \frac { \pi } { 3 } \text {, shitt: } \frac { \pi } { 6 } \text { to the left }$

Question 4

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is maximum at time $t = 0$.amplitude $2.5 \mathrm {~m}$, frequency $750 \mathrm {~Hz}$

Accepted Answer

A)  $y = 2.5 \sin 750 \pi t$ 
B)  $y = 2.5 \sin 1500 \pi t$ 
C)  $y = 2.5 \sin 1500 t$ 
D)  $y = 2.5 \cos 750 \pi t$ 
E)  none of these 
A)  $y = 2.5 \sin 750 \pi t$ 
B)  $y = 2.5 \sin 1500 \pi t$ 
C)  $y = 2.5 \sin 1500 t$ 
D)  $y = 2.5 \cos 750 \pi t$ 
E)  none of these

Question 5

Find the reference number and the terminal point $P ( x , y )$ determined by $t = \frac { 11 \pi } { 6 }$ .

Accepted Answer

The answer of Find the reference number and the terminal...

Question 6

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion

Accepted Answer

A)  $\frac { 1 } { 3 \pi }$ 
B)  $\frac { 1 } { 6 \pi }$ 
C)  $6 \pi$ 
D)  $3 \pi$ 
E)  $2 \pi$ 
A)  $\frac { 1 } { 3 \pi }$ 
B)  $\frac { 1 } { 6 \pi }$ 
C)  $6 \pi$ 
D)  $3 \pi$ 
E)  $2 \pi$

Question 7

Find the reference number and the terminal point $p( x , y )$  determined by $t = \frac { 11 \pi } { 6 }$  .

Accepted Answer

The answer of Find the reference number and the terminal...

Question 8

Find the sign of $\cos t \sin t$ and $\text { sect }$If the terminal point determined by $t$Isinquadrant II

Accepted Answer

A)  $+ , -$ 
B)  $- , +$ 
C)  $- , -$ 
D)  $+ , +$ 
E)  $+ \text {, undefined }$ 
A)  $+ , -$ 
B)  $- , +$ 
C)  $- , -$ 
D)  $+ , +$ 
E)  $+ \text {, undefined }$

Question 9

If the terminal point determined by t is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$, find $\sin t$, $\cos t$And $\tan t$

Accepted Answer

A)  $\sin ( t ) = \frac { 12 } { 13 }$, $\cos \left( t ^ { \prime } \right) = \frac { 5 } { 13 }$, $\tan ( t ) = \frac { 5 } { 12 }$ 
B)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos (t)=\frac{12}{13}$, $\tan ( t ) = - \frac { 5 } { 12 }$ 
C)  $\sin ( t ) = \frac { 5 } { 13 }$, $\cos ( t ) = - \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 13 } { 12 }$ 
D)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 12 } { 5 }$ 
E)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos = \frac { 12 } { 13 }$, $\text { tant } t = \frac { 12 } { 5 }$ 
A)  $\sin ( t ) = \frac { 12 } { 13 }$, $\cos \left( t ^ { \prime } \right) = \frac { 5 } { 13 }$, $\tan ( t ) = \frac { 5 } { 12 }$ 
B)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos (t)=\frac{12}{13}$, $\tan ( t ) = - \frac { 5 } { 12 }$ 
C)  $\sin ( t ) = \frac { 5 } { 13 }$, $\cos ( t ) = - \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 13 } { 12 }$ 
D)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 12 } { 5 }$ 
E)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos = \frac { 12 } { 13 }$, $\text { tant } t = \frac { 12 } { 5 }$

Question 10

Find the exact value of $\sec \left( \frac { 3 \pi } { 4 } \right)$ and $\csc \left( - \frac { 11 \pi } { 4 } \right)$ .

Accepted Answer

The answer of Find the exact value of \(\sec \left(...

Question 11

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find frequency of motion

Accepted Answer

A)  $\frac { 1 } { 3 \pi }$ 
B)  $\frac { 1 } { 6 \pi }$ 
C)  $6 \pi$ 
D)  $3 \pi$ 
E)  $2 \pi$ 
A)  $\frac { 1 } { 3 \pi }$ 
B)  $\frac { 1 } { 6 \pi }$ 
C)  $6 \pi$ 
D)  $3 \pi$ 
E)  $2 \pi$

Question 12

Show that the point $\left( \frac { 1 } { - 15 } , - \frac { 2 } { \sqrt { 5 } } \right)$ is on the unit circle.

Accepted Answer

The answer of Show that the point \(\left( \frac {...

Question 13

Find the vertical asymptotes for the function $y = \tan 2 x$ 
in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ 
.

Accepted Answer

The answer of Find the vertical asymptotes for the function...

Question 14

If the terminal point determined by $t$ is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$, find $\sin t$, $\cos t$and $\tan t$

Accepted Answer

A)  $\sin ( t ) = \frac { 12 } { 13 }$, $\cos ( t ) = \frac { 5 } { 13 }$, $\tan ( t ) = \frac { 5 } { 12 }$ 
B)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 5 } { 12 }$ 
C)  $\sin ( t ) = \frac { 5 } { 13 }$, $\cos ( t ) = - \frac { 12 } { \Gamma 3 }$, $\tan ( t ) = - \frac { 13 } { 12 }$ 
D)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 12 } { 5 }$ 
E)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan t = \frac { 12 } { 5 }$ 
A)  $\sin ( t ) = \frac { 12 } { 13 }$, $\cos ( t ) = \frac { 5 } { 13 }$, $\tan ( t ) = \frac { 5 } { 12 }$ 
B)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 5 } { 12 }$ 
C)  $\sin ( t ) = \frac { 5 } { 13 }$, $\cos ( t ) = - \frac { 12 } { \Gamma 3 }$, $\tan ( t ) = - \frac { 13 } { 12 }$ 
D)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan ( t ) = - \frac { 12 } { 5 }$ 
E)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan t = \frac { 12 } { 5 }$

Question 15

Suppose that the terminal point determined by t is the point $\left( \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$on the unit circle. Find the terminal point determined by $\pi + t$

Accepted Answer

A)  $\left( \frac { 3 } { 3 } , - \frac { 4 } { 5 } \right)$ 
B)  $\left( - \frac { 3 } { 5 } , \frac { 4 } { 5 } \right)$ 
C)  $\left( \frac { 3 } { 4 } , - \frac { 4 } { 3 } \right)$ 
D)  $( - 1,1 )$ 
E)  $\left( - \frac { 4 } { 5 } , \frac { 3 } { 5 } \right)$ 
A)  $\left( \frac { 3 } { 3 } , - \frac { 4 } { 5 } \right)$ 
B)  $\left( - \frac { 3 } { 5 } , \frac { 4 } { 5 } \right)$ 
C)  $\left( \frac { 3 } { 4 } , - \frac { 4 } { 3 } \right)$ 
D)  $( - 1,1 )$ 
E)  $\left( - \frac { 4 } { 5 } , \frac { 3 } { 5 } \right)$

Question 16

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\cot t + \csc t$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  $2$ 
D)  $\frac { 1 } { 2 }$ 
E)  $- \frac { 5 } { 4 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  $2$ 
D)  $\frac { 1 } { 2 }$ 
E)  $- \frac { 5 } { 4 }$

Question 17

Find the exact value of $\sec \left( - \frac { 5 \pi } { 2 } \right)$ and $\csc \left( - \frac { 7 \pi } { 2 } \right)$

Accepted Answer

A)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = 0 , \csc \left( - \frac { 7 \pi } { 2 } \right) = 1$ 
B)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = 0 , \csc \left( - \frac { 7 \pi } { 2 } \right) = - 1$ 
C)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = 1 , \csc \left( - \frac { 7 \pi } { 2 } \right) = \text { undefined }$ 
D)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = \text { undefined, } \csc \left( - \frac { 7 \pi } { 2 } \right) = 1$ 
E)  none of these 
A)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = 0 , \csc \left( - \frac { 7 \pi } { 2 } \right) = 1$ 
B)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = 0 , \csc \left( - \frac { 7 \pi } { 2 } \right) = - 1$ 
C)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = 1 , \csc \left( - \frac { 7 \pi } { 2 } \right) = \text { undefined }$ 
D)  $\sec \left( - \frac { 5 \pi } { 2 } \right) = \text { undefined, } \csc \left( - \frac { 7 \pi } { 2 } \right) = 1$ 
E)  none of these

Question 18

Find the period of the function $y = \frac { 1 } { 4 } \tan \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right)$

Accepted Answer

A)  $2 \pi$ 
B)  $4 \pi$ 
C)  $\pi$ 
D)  $8 \pi$ 
E)  $\frac { \pi } { 2 }$ 
A)  $2 \pi$ 
B)  $4 \pi$ 
C)  $\pi$ 
D)  $8 \pi$ 
E)  $\frac { \pi } { 2 }$

Question 19

Suppose that the terminal point determined by t is the point $\left( \frac { 5 } { 13 } , \frac { 12 } { 13 } \right)$ on the unit circle. Find the terminal point determined by $2 \pi - t$ .

Accepted Answer

The answer of Suppose that the terminal point determined by...

Question 20

Suppose that point $P \left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)$ is on the unit circle. Find $\sin t$and $\cos t$

Accepted Answer

A)  $\sin t = - 2 \sqrt { 2 } , \quad \cos t = 3$ 
B)  $\sin t = - 2 \sqrt { 3 } , \cos t = 3$ 
C)  $\sin t = - \frac { 2 \sqrt { 3 } } { 3 } , \cos t = - \frac { 1 } { 3 }$ 
D)  $\sin t = - \frac { 1 } { 3 } , \quad \cos t = - \frac { 2 - \sqrt { 2 } } { 3 }$ 
E)  none of these 
A)  $\sin t = - 2 \sqrt { 2 } , \quad \cos t = 3$ 
B)  $\sin t = - 2 \sqrt { 3 } , \cos t = 3$ 
C)  $\sin t = - \frac { 2 \sqrt { 3 } } { 3 } , \cos t = - \frac { 1 } { 3 }$ 
D)  $\sin t = - \frac { 1 } { 3 } , \quad \cos t = - \frac { 2 - \sqrt { 2 } } { 3 }$ 
E)  none of these

Find to two decimal places the approximate value of $\tan ( 1.5 )$

Suppose that point $P \left( \frac { \sqrt { 5 } } { 5 } , - \frac { 2 \sqrt { 5 } } { 5 } \right)$ is on the unit circle. Find $\sin t$ and $\cos t$

Find the period and the shift for the function $y = 2 \cot \left( 3 x - \frac { \pi } { 2 } \right)$

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is maximum at time $t = 0$ .amplitude $2.5 \mathrm {~m}$ , frequency $750 \mathrm {~Hz}$

Find the reference number and the terminal point $P ( x , y )$ determined by $t = \frac { 11 \pi } { 6 }$ .

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion

Find the reference number and the terminal point $p( x , y )$ determined by $t = \frac { 11 \pi } { 6 }$ .

Find the sign of $\cos t \sin t$ and $\text { sect }$ If the terminal point determined by $t$ Isinquadrant II

If the terminal point determined by t is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$ , find $\sin t$ , $\cos t$ And $\tan t$

Find the exact value of $\sec \left( \frac { 3 \pi } { 4 } \right)$ and $\csc \left( - \frac { 11 \pi } { 4 } \right)$ .

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find frequency of motion

Show that the point $\left( \frac { 1 } { - 15 } , - \frac { 2 } { \sqrt { 5 } } \right)$ is on the unit circle.

Find the vertical asymptotes for the function $y = \tan 2 x$ in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ .

If the terminal point determined by $t$ is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$ , find $\sin t$ , $\cos t$ and $\tan t$

Suppose that the terminal point determined by t is the point $\left( \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$ on the unit circle. Find the terminal point determined by $\pi + t$

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\cot t + \csc t$

Find the exact value of $\sec \left( - \frac { 5 \pi } { 2 } \right)$ and $\csc \left( - \frac { 7 \pi } { 2 } \right)$

Find the period of the function $y = \frac { 1 } { 4 } \tan \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right)$

Suppose that the terminal point determined by t is the point $\left( \frac { 5 } { 13 } , \frac { 12 } { 13 } \right)$ on the unit circle. Find the terminal point determined by $2 \pi - t$ .

Suppose that point $P \left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)$ is on the unit circle. Find $\sin t$ and $\cos t$

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Exam 7: Conic Sections

Find to two decimal places the approximate value of tan⁡(1.5)\tan ( 1.5 )tan(1.5)

Suppose that point P(55,−255)P \left( \frac { \sqrt { 5 } } { 5 } , - \frac { 2 \sqrt { 5 } } { 5 } \right)P(55​​,−525​​) is on the unit circle. Find sin⁡t\sin tsint and cos⁡t\cos tcost

Find the period and the shift for the function y=2cot⁡(3x−π2)y = 2 \cot \left( 3 x - \frac { \pi } { 2 } \right)y=2cot(3x−2π​)

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is maximum at time t=0t = 0t=0 .amplitude 2.5 m2.5 \mathrm {~m}2.5 m , frequency 750 Hz750 \mathrm {~Hz}750 Hz

Find the reference number and the terminal point P(x,y)P ( x , y )P(x,y) determined by t=11π6t = \frac { 11 \pi } { 6 }t=611π​ .

The function y=−2cos⁡(t3)y = - 2 \cos \left( \frac { t } { 3 } \right)y=−2cos(3t​) models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion

Find the reference number and the terminal point p(x,y)p( x , y )p(x,y) determined by t=11π6t = \frac { 11 \pi } { 6 }t=611π​ .

Find the sign of cos⁡tsin⁡t\cos t \sin tcostsint and sect \text { sect } sect If the terminal point determined by ttt Isinquadrant II

If the terminal point determined by t is (1213,−513)\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)(1312​,−135​) , find sin⁡t\sin tsint , cos⁡t\cos tcost And tan⁡t\tan ttant

Find the exact value of sec⁡(3π4)\sec \left( \frac { 3 \pi } { 4 } \right)sec(43π​) and csc⁡(−11π4)\csc \left( - \frac { 11 \pi } { 4 } \right)csc(−411π​) .

The function y=−2cos⁡(t3)y = - 2 \cos \left( \frac { t } { 3 } \right)y=−2cos(3t​) models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find frequency of motion

Show that the point (1−15,−25)\left( \frac { 1 } { - 15 } , - \frac { 2 } { \sqrt { 5 } } \right)(−151​,−5​2​) is on the unit circle.

Find the vertical asymptotes for the function y=tan⁡2xy = \tan 2 xy=tan2x in the interval (−π2,π2)\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)(−2π​,2π​) .

If the terminal point determined by ttt is (1213,−513)\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)(1312​,−135​) , find sin⁡t\sin tsint , cos⁡t\cos tcost and tan⁡t\tan ttant

Suppose that the terminal point determined by t is the point (35,−45)\left( \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)(53​,−54​) on the unit circle. Find the terminal point determined by π+t\pi + tπ+t

If cos⁡t=35\cos t = \frac { 3 } { 5 }cost=53​ and the terminal point for t is in quadrant IV, find cot⁡t+csc⁡t\cot t + \csc tcott+csct

Find the exact value of sec⁡(−5π2)\sec \left( - \frac { 5 \pi } { 2 } \right)sec(−25π​) and csc⁡(−7π2)\csc \left( - \frac { 7 \pi } { 2 } \right)csc(−27π​)

Find the period of the function y=14tan⁡(x2+π8)y = \frac { 1 } { 4 } \tan \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right)y=41​tan(2x​+8π​)

Suppose that the terminal point determined by t is the point (513,1213)\left( \frac { 5 } { 13 } , \frac { 12 } { 13 } \right)(135​,1312​) on the unit circle. Find the terminal point determined by 2π−t2 \pi - t2π−t .

Suppose that point P(−223,−13)P \left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)P(−322​​,−31​) is on the unit circle. Find sin⁡t\sin tsint and cos⁡t\cos tcost

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Find to two decimal places the approximate value of $\tan ( 1.5 )$

Suppose that point $P \left( \frac { \sqrt { 5 } } { 5 } , - \frac { 2 \sqrt { 5 } } { 5 } \right)$ is on the unit circle. Find $\sin t$ and $\cos t$

Find the period and the shift for the function $y = 2 \cot \left( 3 x - \frac { \pi } { 2 } \right)$

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is maximum at time $t = 0$ .amplitude $2.5 \mathrm {~m}$ , frequency $750 \mathrm {~Hz}$

Find the reference number and the terminal point $P ( x , y )$ determined by $t = \frac { 11 \pi } { 6 }$ .

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion

Find the reference number and the terminal point $p( x , y )$ determined by $t = \frac { 11 \pi } { 6 }$ .

Find the sign of $\cos t \sin t$ and $\text { sect }$ If the terminal point determined by $t$ Isinquadrant II

If the terminal point determined by t is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$ , find $\sin t$ , $\cos t$ And $\tan t$

Find the exact value of $\sec \left( \frac { 3 \pi } { 4 } \right)$ and $\csc \left( - \frac { 11 \pi } { 4 } \right)$ .

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find frequency of motion

Show that the point $\left( \frac { 1 } { - 15 } , - \frac { 2 } { \sqrt { 5 } } \right)$ is on the unit circle.

Find the vertical asymptotes for the function $y = \tan 2 x$ in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ .

If the terminal point determined by $t$ is $\left( \frac { 12 } { 13 } , - \frac { 5 } { 13 } \right)$ , find $\sin t$ , $\cos t$ and $\tan t$

Suppose that the terminal point determined by t is the point $\left( \frac { 3 } { 5 } , - \frac { 4 } { 5 } \right)$ on the unit circle. Find the terminal point determined by $\pi + t$

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\cot t + \csc t$

Find the exact value of $\sec \left( - \frac { 5 \pi } { 2 } \right)$ and $\csc \left( - \frac { 7 \pi } { 2 } \right)$

Find the period of the function $y = \frac { 1 } { 4 } \tan \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right)$

Suppose that the terminal point determined by t is the point $\left( \frac { 5 } { 13 } , \frac { 12 } { 13 } \right)$ on the unit circle. Find the terminal point determined by $2 \pi - t$ .

Suppose that point $P \left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)$ is on the unit circle. Find $\sin t$ and $\cos t$