Question 1

The point $P ( x , y )$ 
is on the unit circle in quadrant II. If $x = - \sqrt { 11 } / 6$ 
find y.

Accepted Answer

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

Question 2

Determine whether the function is even, odd, or neither. $y = 2 \sin x \cos x$

Accepted Answer

The answer of Determine whether the function is even, odd,...

Question 3

Which function has y-axis symmetry?

Accepted Answer

A)  $y = \tan x$ 
B)  $y = \csc x$ 
C)  $y = \cot x$ 
D)  $y = \sec x$ 
E)  all have y-axis symmetry 
A)  $y = \tan x$ 
B)  $y = \csc x$ 
C)  $y = \cot x$ 
D)  $y = \sec x$ 
E)  all have y-axis symmetry

Question 4

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

Accepted Answer

Amplitude

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

The answer of Show that the point \(( 1 /...

Question 7

Use a graphing device to find the maximum and minimum values of the function $y = \cos x - \frac { 1 } { 2 } \cos 2 x$

Accepted Answer

A) maximum value: $\frac { 4 } { 3 }$
, minimum value: $0$ 
B) maximum value: $\frac { 3 } { 4 }$
, minimum value: $- 1$ 
C) maximum value: $\frac { 3 } { 4 }$
, minimum value: $- \frac { 3 } { 2 }$ 
D) maximum value: $\frac { 3 } { 4 }$
, minimum value: $- \frac { 4 } { 3 }$ 
E)  none of these 
A) maximum value: $\frac { 4 } { 3 }$
, minimum value: $0$ 
B) maximum value: $\frac { 3 } { 4 }$
, minimum value: $- 1$ 
C) maximum value: $\frac { 3 } { 4 }$
, minimum value: $- \frac { 3 } { 2 }$ 
D) maximum value: $\frac { 3 } { 4 }$
, minimum value: $- \frac { 4 } { 3 }$ 
E)  none of these

Question 8

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\text { tant } t + \operatorname { Sec } t$ .

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find the exact value of the expression, if it is defined. $\tan ^ { - 1 } ( \tan ( - \pi / 4 ) )$

Accepted Answer

The answer of Find the exact value of the expression,...

Question 11

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)  $\frac { 1 } { \cos ^ { 3 } t }$ 
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)  $\frac { 1 } { \cos ^ { 3 } t }$

Question 12

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

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

Question 13

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

Accepted Answer

A)  $\tan ( 1.5 ) \approx 0.261$ 
B)  $\tan ( 1.5 ) \approx 0.026$ 
C)  $\tan ( 1.5 ) \approx 14.101$ 
D)  $\tan ( 1.5 ) \approx 1.410$ 
E)  none 
A)  $\tan ( 1.5 ) \approx 0.261$ 
B)  $\tan ( 1.5 ) \approx 0.026$ 
C)  $\tan ( 1.5 ) \approx 14.101$ 
D)  $\tan ( 1.5 ) \approx 1.410$ 
E)  none

Question 14

The point $P ( x , y )$ is on the unit circle in quadrant IV. If $x = \sqrt { 11 } / 6$ 
find y.

Accepted Answer

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

Question 15

Find the amplitude, period and phase shift of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$

Accepted Answer

A) amplitude: $2$, period: $\pi$, phase shift: $3 / 4$ 
B) amplitude: $- 2$, period: $\pi$, phase shift: $3 / 2$ 
C) amplitude: $4$, period: $2 \pi$, phase shift: $1$ 
D) amplitude: $- 2$, period: $4 \pi$, phase shift: $3 / 4$ 
E)  amplitude: $1 / 2$, period: $\pi$, phase shift: $3 / 4$ 
A) amplitude: $2$, period: $\pi$, phase shift: $3 / 4$ 
B) amplitude: $- 2$, period: $\pi$, phase shift: $3 / 2$ 
C) amplitude: $4$, period: $2 \pi$, phase shift: $1$ 
D) amplitude: $- 2$, period: $4 \pi$, phase shift: $3 / 4$ 
E)  amplitude: $1 / 2$, period: $\pi$, phase shift: $3 / 4$

Question 16

Show that the point $\left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)$ is on the unit circle.

Accepted Answer

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

Question 17

If $605 t = 3 / 5$ and the terminal point for t is in quadrant IV, find $\tan t + \mathrm { sec } t$ .

Accepted Answer

The answer of If $605 t = 3 / 5$...

Question 18

Use a graphing device to find the maximum and minimum values of the function $y = \cos x - \frac { 1 } { 2 } \cos 2 x$ .

Accepted Answer

The maximu

Question 19

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

Accepted Answer

The answer of Determine whether the function is even, odd,...

Question 20

Find the period of the function $y = 3 \sec x$

Accepted Answer

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

The point $P ( x , y )$ is on the unit circle in quadrant II. If $x = - \sqrt { 11 } / 6$ find y.

Determine whether the function is even, odd, or neither. $y = 2 \sin x \cos x$

Which function has y-axis symmetry?

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

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

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

Use a graphing device to find the maximum and minimum values of the function $y = \cos x - \frac { 1 } { 2 } \cos 2 x$

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\text { tant } t + \operatorname { Sec } t$ .

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

Find the exact value of the expression, if it is defined. $\tan ^ { - 1 } ( \tan ( - \pi / 4 ) )$

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

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

The point $P ( x , y )$ is on the unit circle in quadrant IV. If $x = \sqrt { 11 } / 6$ find y.

Find the amplitude, period and phase shift of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$

Show that the point $\left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)$ is on the unit circle.

If $605 t = 3 / 5$ and the terminal point for t is in quadrant IV, find $\tan t + \mathrm { sec } t$ .

Use a graphing device to find the maximum and minimum values of the function $y = \cos x - \frac { 1 } { 2 } \cos 2 x$ .

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

Find the period of the function $y = 3 \sec x$

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

Exam 7: Conic Sections

The point P(x,y)P ( x , y )P(x,y) is on the unit circle in quadrant II. If x=−11/6x = - \sqrt { 11 } / 6x=−11​/6 find y.

Determine whether the function is even, odd, or neither. y=2sin⁡xcos⁡xy = 2 \sin x \cos xy=2sinxcosx

Which function has y-axis symmetry?

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 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​

Show that the point (1/5,−2/5)( 1 / \sqrt { 5 } , - 2 / \sqrt { 5 } )(1/5​,−2/5​) is on the unit circle.

Use a graphing device to find the maximum and minimum values of the function y=cos⁡x−12cos⁡2xy = \cos x - \frac { 1 } { 2 } \cos 2 xy=cosx−21​cos2x

If cos⁡t=35\cos t = \frac { 3 } { 5 }cost=53​ and the terminal point for t is in quadrant IV, find tant t+Sec⁡t\text { tant } t + \operatorname { Sec } t tant t+Sect .

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

Find the exact value of the expression, if it is defined. tan⁡−1(tan⁡(−π/4))\tan ^ { - 1 } ( \tan ( - \pi / 4 ) )tan−1(tan(−π/4))

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

The point P(x,y)P ( x , y )P(x,y) is on the unit circle in quadrant IV. If x=11/6x = \sqrt { 11 } / 6x=11​/6 find y.

Find the amplitude, period and phase shift of y=−2sin⁡(2x−32)y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)y=−2sin(2x−23​)

Show that the point (−223,−13)\left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)(−322​​,−31​) is on the unit circle.

If 605t=3/5605 t = 3 / 5605t=3/5 and the terminal point for t is in quadrant IV, find tan⁡t+sect\tan t + \mathrm { sec } ttant+sect .

Use a graphing device to find the maximum and minimum values of the function y=cos⁡x−12cos⁡2xy = \cos x - \frac { 1 } { 2 } \cos 2 xy=cosx−21​cos2x .

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=3sec⁡xy = 3 \sec xy=3secx

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

The point $P ( x , y )$ is on the unit circle in quadrant II. If $x = - \sqrt { 11 } / 6$ find y.

Determine whether the function is even, odd, or neither. $y = 2 \sin x \cos x$

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

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

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

Use a graphing device to find the maximum and minimum values of the function $y = \cos x - \frac { 1 } { 2 } \cos 2 x$

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\text { tant } t + \operatorname { Sec } t$ .

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

Find the exact value of the expression, if it is defined. $\tan ^ { - 1 } ( \tan ( - \pi / 4 ) )$

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

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

The point $P ( x , y )$ is on the unit circle in quadrant IV. If $x = \sqrt { 11 } / 6$ find y.

Find the amplitude, period and phase shift of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$

Show that the point $\left( - \frac { 2 \sqrt { 2 } } { 3 } , - \frac { 1 } { 3 } \right)$ is on the unit circle.

If $605 t = 3 / 5$ and the terminal point for t is in quadrant IV, find $\tan t + \mathrm { sec } t$ .

Use a graphing device to find the maximum and minimum values of the function $y = \cos x - \frac { 1 } { 2 } \cos 2 x$ .

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

Find the period of the function $y = 3 \sec x$