Question 1

Find the exact value of each expression, if it is defined
a) $\sin ^ { - 1 } ( - 2 )$

b) $\cos ^ { - 1 } ( - \sqrt { 3 } )$ c) $\tan ^ { - 1 } ( - 1 )$

Accepted Answer

not define

Question 2

Find the amplitude, period, and phase shift of the function. $y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)$

Accepted Answer

A)  Amplitude 1/2, Period $4 \pi$, phase shift $\pi / 3$ 
B)  Amplitude 1/2, Period $2 \pi$, phase shift $\pi / 3$ 
C)  Amplitude 2, Period $\pi$, phase shift $\pi / 6$ 
D)  Amplitude 2, Period $4 \pi$, phase shift $\pi / 6$ 
E)  Amplitude 2, Period $4 \pi$, phase shift $\pi / 3$ 
A)  Amplitude 1/2, Period $4 \pi$, phase shift $\pi / 3$ 
B)  Amplitude 1/2, Period $2 \pi$, phase shift $\pi / 3$ 
C)  Amplitude 2, Period $\pi$, phase shift $\pi / 6$ 
D)  Amplitude 2, Period $4 \pi$, phase shift $\pi / 6$ 
E)  Amplitude 2, Period $4 \pi$, phase shift $\pi / 3$

Question 3

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

Accepted Answer

The answer of Find $\text { sect }$ given that...

Question 4

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is zero at time $t = 0$ 
.amplitude 10 in, frequency $2 \mathrm {~Hz}$

Accepted Answer

The answer of Find a function that models simple harmonic...

Question 5

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

Accepted Answer

A)  $0.260$ 
B)  $0.026$ 
C)  $14.101$ 
D)  $1.410$ 
E)  none 
A)  $0.260$ 
B)  $0.026$ 
C)  $14.101$ 
D)  $1.410$ 
E)  none

Question 6

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

Accepted Answer

The answer of If \(\cos t = \frac { 3...

Question 7

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)  $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
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)  $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
E)  $\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \mid \right.$

Question 8

Sketch the graph of the function. $y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Express $\tan t$ in terms of $\sin t$ , if the terminal point determined by t is in quadrant III.

Accepted Answer

The answer of Express $\tan t$ in terms of \(\sin...

Question 10

Use the fundamental identities to write the first expression in terms of the second. $\frac { \cot t } { \sin t } , \cos t$

Accepted Answer

The answer of Use the fundamental identities to write the...

Question 11

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

Accepted Answer

The maximu

Question 12

Find the exact value of the expression, if it is defined. $\cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right]$

Accepted Answer

A)  $- 1 / 2$ 
B)  $\sqrt { 3 } / 3$ 
C)  $\sqrt { 3 }$ 
D)  $\sqrt { 3 } / 2$ 
E)  $1 / 2$ 
A)  $- 1 / 2$ 
B)  $\sqrt { 3 } / 3$ 
C)  $\sqrt { 3 }$ 
D)  $\sqrt { 3 } / 2$ 
E)  $1 / 2$

Question 13

The point $P ( x , y )$ is on the unit circle in quadrant IV. If $y = - 5 / 6$ find x.

Accepted Answer

The answer of The point \(P ( x , y...

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

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

Question 15

Find the exact value of $\sin ( 2 \pi )$ and $\cos ( - 2 \pi )$

Accepted Answer

A)  $\sin ( 2 \pi ) = 1 , \quad \cos ( - 2 \pi ) = - 1$ 
B)  $\sin ( 2 \pi ) = 0 , \quad \cos ( - 2 \pi ) = - 1$ 
C)  $\sin ( 2 \pi ) = 1 , \quad \cos ( - 2 \pi ) = 0$ 
D)  $\sin ( 2\pi ) = 0 , \quad \cos ( - 2 \pi ) = - 1$ 
E)  none of these 
A)  $\sin ( 2 \pi ) = 1 , \quad \cos ( - 2 \pi ) = - 1$ 
B)  $\sin ( 2 \pi ) = 0 , \quad \cos ( - 2 \pi ) = - 1$ 
C)  $\sin ( 2 \pi ) = 1 , \quad \cos ( - 2 \pi ) = 0$ 
D)  $\sin ( 2\pi ) = 0 , \quad \cos ( - 2 \pi ) = - 1$ 
E)  none of these

Question 16

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 amplitude, period, and frequency of motion and sketch a graph of the function over one complete period.

Accepted Answer

amplitude

Question 17

Express $\tan t$ 
in terms of $\sin t$ 
, if the terminal point determined by t is in quadrant III.

Accepted Answer

The answer of Express $\tan t$ 
in terms of \(\sin...

Question 18

Find the period of the function $y = 3 \sec x$  and sketch its graph.

Accepted Answer

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

Question 19

Find $\tan t$ given that $\sin t = - \frac { 3 } { 5 }$ and $\mathrm { cot } t < 0$ .

Accepted Answer

The answer of Find $\tan t$ given that \(\sin t...

Question 20

Find the exact value of $\text { Sec } \left( \frac { 3 \pi } { 4 } \right)$ and $\operatorname { CSC } \left( - \frac { 11 \pi } { 4 } \right)$ .

Accepted Answer

The answer of Find the exact value of \(\text {...

Find the exact value of each expression, if it is defined a) $\sin ^ { - 1 } ( - 2 )$ b) $\cos ^ { - 1 } ( - \sqrt { 3 } )$ c) $\tan ^ { - 1 } ( - 1 )$

Find the amplitude, period, and phase shift of the function. $y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)$

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

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is zero at time $t = 0$ .amplitude 10 in, frequency $2 \mathrm {~Hz}$

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

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

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 $\pi - t$

Sketch the graph of the function. $y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)$

Express $\tan t$ in terms of $\sin t$ , if the terminal point determined by t is in quadrant III.

Use the fundamental identities to write the first expression in terms of the second. $\frac { \cot t } { \sin t } , \cos t$

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

Find the exact value of the expression, if it is defined. $\cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right]$

The point $P ( x , y )$ is on the unit circle in quadrant IV. If $y = - 5 / 6$ find x.

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 $\sin ( 2 \pi )$ and $\cos ( - 2 \pi )$

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 amplitude, period, and frequency of motion and sketch a graph of the function over one complete period.

Express $\tan t$ in terms of $\sin t$ , if the terminal point determined by t is in quadrant III.

Find the period of the function $y = 3 \sec x$ and sketch its graph.

Find $\tan t$ given that $\sin t = - \frac { 3 } { 5 }$ and $\mathrm { cot } t < 0$ .

Find the exact value of $\text { Sec } \left( \frac { 3 \pi } { 4 } \right)$ and $\operatorname { CSC } \left( - \frac { 11 \pi } { 4 } \right)$ .

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Exam 7: Conic Sections

Find the exact value of each expression, if it is defined a) sin⁡−1(−2)\sin ^ { - 1 } ( - 2 )sin−1(−2) b) cos⁡−1(−3)\cos ^ { - 1 } ( - \sqrt { 3 } )cos−1(−3​) c) tan⁡−1(−1)\tan ^ { - 1 } ( - 1 )tan−1(−1)

Find the amplitude, period, and phase shift of the function. y=2cos⁡(12x−π6)y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)y=2cos(21​x−6π​)

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 a function that models simple harmonic motion having the given properties. Assume that the displacement is zero at time t=0t = 0t=0 .amplitude 10 in, frequency 2 Hz2 \mathrm {~Hz}2 Hz

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

If cos⁡t=35\cos t = \frac { 3 } { 5 }cost=53​ and the terminal point for t is in quadrant IV, find tan⁡t+sect\tan t + \mathrm { sec } ttant+sect .

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

Sketch the graph of the function. y=2cos⁡(4x−π2)y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)y=2cos(4x−2π​)

Express tan⁡t\tan ttant in terms of sin⁡t\sin tsint , if the terminal point determined by t is in quadrant III.

Use the fundamental identities to write the first expression in terms of the second. cot⁡tsin⁡t,cos⁡t\frac { \cot t } { \sin t } , \cos tsintcott​,cost

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 exact value of the expression, if it is defined. cos⁡(tan⁡−1(−3)]\cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right]cos(tan−1(−3​)]

The point P(x,y)P ( x , y )P(x,y) is on the unit circle in quadrant IV. If y=−5/6y = - 5 / 6y=−5/6 find x.

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 .

Find the exact value of sin⁡(2π)\sin ( 2 \pi )sin(2π) and cos⁡(−2π)\cos ( - 2 \pi )cos(−2π)

Express tan⁡t\tan ttant in terms of sin⁡t\sin tsint , if the terminal point determined by t is in quadrant III.

Find the period of the function y=3sec⁡xy = 3 \sec xy=3secx and sketch its graph.

Find tan⁡t\tan ttant given that sin⁡t=−35\sin t = - \frac { 3 } { 5 }sint=−53​ and cott<0\mathrm { cot } t < 0cott<0 .

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

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Find the exact value of each expression, if it is defined a) $\sin ^ { - 1 } ( - 2 )$ b) $\cos ^ { - 1 } ( - \sqrt { 3 } )$ c) $\tan ^ { - 1 } ( - 1 )$

Find the amplitude, period, and phase shift of the function. $y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)$

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

Find a function that models simple harmonic motion having the given properties. Assume that the displacement is zero at time $t = 0$ .amplitude 10 in, frequency $2 \mathrm {~Hz}$

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

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

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 $\pi - t$

Sketch the graph of the function. $y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)$

Express $\tan t$ in terms of $\sin t$ , if the terminal point determined by t is in quadrant III.

Use the fundamental identities to write the first expression in terms of the second. $\frac { \cot t } { \sin t } , \cos t$

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

Find the exact value of the expression, if it is defined. $\cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right]$

The point $P ( x , y )$ is on the unit circle in quadrant IV. If $y = - 5 / 6$ find x.

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 $\sin ( 2 \pi )$ and $\cos ( - 2 \pi )$

Express $\tan t$ in terms of $\sin t$ , if the terminal point determined by t is in quadrant III.

Find the period of the function $y = 3 \sec x$ and sketch its graph.

Find $\tan t$ given that $\sin t = - \frac { 3 } { 5 }$ and $\mathrm { cot } t < 0$ .

Find the exact value of $\text { Sec } \left( \frac { 3 \pi } { 4 } \right)$ and $\operatorname { CSC } \left( - \frac { 11 \pi } { 4 } \right)$ .