Question 1

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

Accepted Answer

A)  $- \frac { \pi } { 6 }$, $P ( x , y ) = \left( \frac { - \sqrt { 5 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
B)  $\pi$, $P ( x , y ) = ( - 1,0 )$ 
C)  $\frac { \pi } { 6 }$, $D ( x , y ) = \left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  $\frac { \pi } { 3 }$, $p ( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 5 } } { 2 } \right)$ 
E)  $\frac { 11 \pi } { 6 }$, $p ( x , y ) = \left( - \frac { - \sqrt {5 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
A)  $- \frac { \pi } { 6 }$, $P ( x , y ) = \left( \frac { - \sqrt { 5 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
B)  $\pi$, $P ( x , y ) = ( - 1,0 )$ 
C)  $\frac { \pi } { 6 }$, $D ( x , y ) = \left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  $\frac { \pi } { 3 }$, $p ( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 5 } } { 2 } \right)$ 
E)  $\frac { 11 \pi } { 6 }$, $p ( x , y ) = \left( - \frac { - \sqrt {5 } } { 2 } , - \frac { 1 } { 2 } \right)$

Question 2

Use a graphing device to find the maximum and minimum values of the function $y = \cos x + \sin 2 x$

Accepted Answer

A) maximum value: $1.1$
, minimum value: $- 1.1$ 
B) maximum value: $- 1.1$
, minimum value: $- 0.76$ 
C) maximum value: $1.76$
, minimum value: $- 1.76$ 
D) maximum value: $2.76$
, minimum value: $- 2.76$ 
E) maximum value: $1.5$
, minimum value: $- 1$ 
A) maximum value: $1.1$
, minimum value: $- 1.1$ 
B) maximum value: $- 1.1$
, minimum value: $- 0.76$ 
C) maximum value: $1.76$
, minimum value: $- 1.76$ 
D) maximum value: $2.76$
, minimum value: $- 2.76$ 
E) maximum value: $1.5$
, minimum value: $- 1$

Question 3

Find the approximate value of $\tan ( 1.5 )$ using a calculator.

Accepted Answer

The answer of Find the approximate value of \(\tan (...

Question 4

Find the vertical asymptotes for the function $y = 3 \sec \frac { 1 } { 2 } x$  in the interval $[ 0,4 \pi ]$  .

Accepted Answer

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

Question 5

Determine whether the function is even, odd, or neither. $y = \sin x + \cos x$

Accepted Answer

A) even 
B) odd 
C) neither 
A) even 
B) odd 
C) neither

Question 6

Find the period of the function $y = \frac { 1 } { 5 } \cot x$

Accepted Answer

A)  $\frac { \pi } { 5 }$ 
B)  $5 \pi$ 
C)  $\pi$ 
D)  $\frac { 2 \pi } { 5 }$ 
E)  $\frac { 5 \pi } { 2 }$ 
A)  $\frac { \pi } { 5 }$ 
B)  $5 \pi$ 
C)  $\pi$ 
D)  $\frac { 2 \pi } { 5 }$ 
E)  $\frac { 5 \pi } { 2 }$

Question 7

Find the period of the function $y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)$  and sketch its graph.

Accepted Answer

The answer of Find the period of the function \(y...

Question 8

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

The answer of If the terminal point determined by t...

Question 9

Find the vertical asymptotes for the function $y = \frac { 1 } { 2 } \csc 2 x$ in the interval $[ - \pi , \pi ]$

Accepted Answer

A)  $x = - \pi , - \frac { \pi } { 2 } , 0 , \frac { \pi } { 2 } , \pi$ 
B)  $x = - \pi , 0 , \pi$ 
C)  $x = - \frac { \pi } { 2 } , 0 , \frac { \pi } { 2 }$ 
D)  $x = - \pi , - \frac { \pi } { 2 } , \frac { \pi } { 2 } , \pi$ 
E)  $x = 0 , \frac { \pi } { 2 } , \pi$ 
A)  $x = - \pi , - \frac { \pi } { 2 } , 0 , \frac { \pi } { 2 } , \pi$ 
B)  $x = - \pi , 0 , \pi$ 
C)  $x = - \frac { \pi } { 2 } , 0 , \frac { \pi } { 2 }$ 
D)  $x = - \pi , - \frac { \pi } { 2 } , \frac { \pi } { 2 } , \pi$ 
E)  $x = 0 , \frac { \pi } { 2 } , \pi$

Question 10

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

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 11

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 $\pi + t$ .

Accepted Answer

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

Question 12

Find $\text { sect }$ given that $\sin t = - \frac { 3 } { 5 }$and $\tan t > 0$

Accepted Answer

A)  $\operatorname { sect } = \frac { 5 } { 3 }$ 
B)  $\sec t = - \frac { 5 } { 3 }$ 
C)  $\sec t = - \frac { 3 } { 4 }$ 
D)  $\sec t = - \frac { 5 } { 4 }$ 
E)  $\operatorname { sect } = \frac { 5 } { 4 }$ 
A)  $\operatorname { sect } = \frac { 5 } { 3 }$ 
B)  $\sec t = - \frac { 5 } { 3 }$ 
C)  $\sec t = - \frac { 3 } { 4 }$ 
D)  $\sec t = - \frac { 5 } { 4 }$ 
E)  $\operatorname { sect } = \frac { 5 } { 4 }$

Question 13

Find period and graph the function. $y = 2 \tan ( 2 x - \pi / 4 )$

Accepted Answer

A)  $\pi / 2$ 
B)  $2 \pi$ 
C)  $\pi$ 
D)  $4 \pi$ 
E)  $1 / 2$ 
A)  $\pi / 2$ 
B)  $2 \pi$ 
C)  $\pi$ 
D)  $4 \pi$ 
E)  $1 / 2$

Question 14

Suppose that the terminal point determined by $t$ is the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$
On the unit circle. Find the terminal point determined by $\pi - t$

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
C)  $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
D)  $\left( - \frac { \sqrt { 5 } } { 2 } , \frac { 1 } { 2 } \right)$ 
E)  $\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \mid \right.$ 
A)  $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
C)  $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
D)  $\left( - \frac { \sqrt { 5 } } { 2 } , \frac { 1 } { 2 } \right)$ 
E)  $\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \mid \right.$

Question 15

Use the fundamental identities to write the first expression in terms of the second. $\tan ^ { 2 } t \sec t , \cos t$

Accepted Answer

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

Question 16

Find the sign of $\cos t \sin t$  if the terminal point determined by $t$ is in quadrant II.

Accepted Answer

The answer of Find the sign of \(\cos t \sin...

Question 17

Find the period of the function $y = \frac { 1 } { 3 } \operatorname { coc } x$ 
and sketch its graph.

Accepted Answer

The answer of Find the period of the function \(y...

Question 18

Sketch the graph of the function $y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)$

Accepted Answer

A)   
B)   
C)   
D)   
E)  none 
A)   
B)   
C)   
D)   
E)  none

Question 19

Graph the function. $y = 2 \tan ( x -  { \pi } / 4 )$

Accepted Answer

A)   
B)   
C)   
D)   
E)  none 
A)   
B)   
C)   
D)   
E)  none

Question 20

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...

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

Use a graphing device to find the maximum and minimum values of the function $y = \cos x + \sin 2 x$

Find the approximate value of $\tan ( 1.5 )$ using a calculator.

Find the vertical asymptotes for the function $y = 3 \sec \frac { 1 } { 2 } x$ in the interval $[ 0,4 \pi ]$ .

Determine whether the function is even, odd, or neither. $y = \sin x + \cos x$

Find the period of the function $y = \frac { 1 } { 5 } \cot x$

Find the period of the function $y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)$ and sketch its graph.

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 vertical asymptotes for the function $y = \frac { 1 } { 2 } \csc 2 x$ in the interval $[ - \pi , \pi ]$

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

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 $\pi + t$ .

Find $\text { sect }$ given that $\sin t = - \frac { 3 } { 5 }$ and $\tan t > 0$

Find period and graph the function. $y = 2 \tan ( 2 x - \pi / 4 )$

Suppose that the terminal point determined by $t$ is the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ On the unit circle. Find the terminal point determined by $\pi - t$

Use the fundamental identities to write the first expression in terms of the second. $\tan ^ { 2 } t \sec t , \cos t$

Find the sign of $\cos t \sin t$ if the terminal point determined by $t$ is in quadrant II.

Find the period of the function $y = \frac { 1 } { 3 } \operatorname { coc } x$ and sketch its graph.

Sketch the graph of the function $y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)$

Graph the function. $y = 2 \tan ( x - { \pi } / 4 )$

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 $2 \pi - t$ .

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Exam 7: Conic Sections

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​

Use a graphing device to find the maximum and minimum values of the function y=cos⁡x+sin⁡2xy = \cos x + \sin 2 xy=cosx+sin2x

Find the approximate value of tan⁡(1.5)\tan ( 1.5 )tan(1.5) using a calculator.

Find the vertical asymptotes for the function y=3sec⁡12xy = 3 \sec \frac { 1 } { 2 } xy=3sec21​x in the interval [0,4π][ 0,4 \pi ][0,4π] .

Determine whether the function is even, odd, or neither. y=sin⁡x+cos⁡xy = \sin x + \cos xy=sinx+cosx

Find the period of the function y=15cot⁡xy = \frac { 1 } { 5 } \cot xy=51​cotx

Find the period of the function y=12tan⁡(x−π3)y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)y=21​tan(x−3π​) and sketch its graph.

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 vertical asymptotes for the function y=12csc⁡2xy = \frac { 1 } { 2 } \csc 2 xy=21​csc2x in the interval [−π,π][ - \pi , \pi ][−π,π]

If cos⁡t=35\cos t = \frac { 3 } { 5 }cost=53​ and the terminal point for t is in quadrant IV, find Cott+CSCt\mathrm { Cot } t + \mathrm { CSC } tCott+CSCt

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 π+t\pi + tπ+t .

Find sect \text { sect } sect given that sin⁡t=−35\sin t = - \frac { 3 } { 5 }sint=−53​ and tan⁡t>0\tan t > 0tant>0

Find period and graph the function. y=2tan⁡(2x−π/4)y = 2 \tan ( 2 x - \pi / 4 )y=2tan(2x−π/4)

Suppose that the terminal point determined by ttt is the point (12,32)\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)(21​,23​​) On the unit circle. Find the terminal point determined by π−t\pi - tπ−t

Use the fundamental identities to write the first expression in terms of the second. tan⁡2tsec⁡t,cos⁡t\tan ^ { 2 } t \sec t , \cos ttan2tsect,cost

Find the sign of cos⁡tsin⁡t\cos t \sin tcostsint if the terminal point determined by ttt is in quadrant II.

Find the period of the function y=13coc⁡xy = \frac { 1 } { 3 } \operatorname { coc } xy=31​cocx and sketch its graph.

Sketch the graph of the function y=12tan⁡(x−π3)y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)y=21​tan(x−3π​)

Graph the function. y=2tan⁡(x−π/4)y = 2 \tan ( x - { \pi } / 4 )y=2tan(x−π/4)

Suppose that the terminal point determined by ttt 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 .

Equations and Graphs

Functions

Polynomial and Rational Functions

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Filters

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

Use a graphing device to find the maximum and minimum values of the function $y = \cos x + \sin 2 x$

Find the approximate value of $\tan ( 1.5 )$ using a calculator.

Find the vertical asymptotes for the function $y = 3 \sec \frac { 1 } { 2 } x$ in the interval $[ 0,4 \pi ]$ .

Determine whether the function is even, odd, or neither. $y = \sin x + \cos x$

Find the period of the function $y = \frac { 1 } { 5 } \cot x$

Find the period of the function $y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)$ and sketch its graph.

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 vertical asymptotes for the function $y = \frac { 1 } { 2 } \csc 2 x$ in the interval $[ - \pi , \pi ]$

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

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 $\pi + t$ .

Find $\text { sect }$ given that $\sin t = - \frac { 3 } { 5 }$ and $\tan t > 0$

Find period and graph the function. $y = 2 \tan ( 2 x - \pi / 4 )$

Suppose that the terminal point determined by $t$ is the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ On the unit circle. Find the terminal point determined by $\pi - t$

Use the fundamental identities to write the first expression in terms of the second. $\tan ^ { 2 } t \sec t , \cos t$

Find the sign of $\cos t \sin t$ if the terminal point determined by $t$ is in quadrant II.

Find the period of the function $y = \frac { 1 } { 3 } \operatorname { coc } x$ and sketch its graph.

Sketch the graph of the function $y = \frac { 1 } { 2 } \tan \left( x - \frac { \pi } { 3 } \right)$

Graph the function. $y = 2 \tan ( x - { \pi } / 4 )$

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 $2 \pi - t$ .