Question 1

Find the reference number for $t = - \frac { \pi } { 6 }$

Accepted Answer

A)  $\bar  { t } = \frac { 11 \pi } { 6 }$ 
B)  $\bar  { t }= - \frac { 5 \pi } { 6 }$ 
C)  $\bar  { t }= \frac { \pi } { 6 }$ 
D)  $\bar { t } = \frac { \pi } { 12 }$ 
E)  $\bar  { t }= - \frac { \pi } { 6 }$ 
A)  $\bar  { t } = \frac { 11 \pi } { 6 }$ 
B)  $\bar  { t }= - \frac { 5 \pi } { 6 }$ 
C)  $\bar  { t }= \frac { \pi } { 6 }$ 
D)  $\bar { t } = \frac { \pi } { 12 }$ 
E)  $\bar  { t }= - \frac { \pi } { 6 }$

Question 2

Find the period of the function $y = \frac { 1 } { 3 } \csc 2 x$

Accepted Answer

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

Question 3

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) max: $\frac { 4 } { 3 }$
, min: $0$ 
B) max: $\frac { 3 } { 4 }$
, min: $- 1$ 
C) max: $\frac { 3 } { 4 }$
, min: $- \frac { 3 } { 2 }$ 
D) max: $\frac { 3 } { 4 }$
, min: $- \frac { 4 } { 3 }$ 
E)  none 
A) max: $\frac { 4 } { 3 }$
, min: $0$ 
B) max: $\frac { 3 } { 4 }$
, min: $- 1$ 
C) max: $\frac { 3 } { 4 }$
, min: $- \frac { 3 } { 2 }$ 
D) max: $\frac { 3 } { 4 }$
, min: $- \frac { 4 } { 3 }$ 
E)  none

Question 4

Find the amplitude, period and phase shift of $y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)$ 
and sketch its graph.

Accepted Answer

Amplitude:

Question 5

Find the amplitude, period, and phase shift of the function. $y = 2 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 3 } \right)$

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Find the reference number for $t = - \frac { 22 \pi } { 3 }$ 
.

Accepted Answer

The answer of Find the reference number for \(t =...

Question 8

Find the reference number for $t = - \frac { 26 \pi } { 5 }$

Accepted Answer

A)  $- \frac { \pi } { 5 }$ 
B)  $\frac { 26 \pi } { 5 }$ 
C)  $- \frac { 13 \pi } { 5 }$ 
D)  $5 \pi$ 
E)  $\frac { \pi } { 5 }$ 
A)  $- \frac { \pi } { 5 }$ 
B)  $\frac { 26 \pi } { 5 }$ 
C)  $- \frac { 13 \pi } { 5 }$ 
D)  $5 \pi$ 
E)  $\frac { \pi } { 5 }$

Question 9

The function $y = 1.6 \sin ( t - 1.8 )$ 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)  $\frac { 1 } { 2 \pi } \text { cycles per second }$ 
B)  $1.6 \text { cycles per second }$ 
C)  $1.8 \text { cycles per second }$ 
D)  $2 \pi \text { cycles per second }$ 
E)  $3.9 \text { cycles per second }$ 
A)  $\frac { 1 } { 2 \pi } \text { cycles per second }$ 
B)  $1.6 \text { cycles per second }$ 
C)  $1.8 \text { cycles per second }$ 
D)  $2 \pi \text { cycles per second }$ 
E)  $3.9 \text { cycles per second }$

Find the reference number for $t = - \frac { \pi } { 6 }$

Find the period of the function $y = \frac { 1 } { 3 } \csc 2 x$

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

Find the amplitude, period and phase shift of $y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)$ and sketch its graph.

Find the amplitude, period, and phase shift of the function. $y = 2 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 3 } \right)$

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

Find the reference number for $t = - \frac { 22 \pi } { 3 }$ .

Find the reference number for $t = - \frac { 26 \pi } { 5 }$

The function $y = 1.6 \sin ( t - 1.8 )$ 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

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

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Filters

Exam 7: Conic Sections

Find the reference number for t=−π6t = - \frac { \pi } { 6 }t=−6π​

Find the period of the function y=13csc⁡2xy = \frac { 1 } { 3 } \csc 2 xy=31​csc2x

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

Find the amplitude, period and phase shift of y=2cos⁡(4x−π2)y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)y=2cos(4x−2π​) and sketch its graph.

Find the amplitude, period, and phase shift of the function. y=2sin⁡(12x−π3)y = 2 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 3 } \right)y=2sin(21​x−3π​)

Find the exact value of each expression, if it is defined. tan⁡−1(3/3)\tan ^ { - 1 } ( \sqrt { 3 } / 3 )tan−1(3​/3)

Find the reference number for t=−22π3t = - \frac { 22 \pi } { 3 }t=−322π​ .

Find the reference number for t=−26π5t = - \frac { 26 \pi } { 5 }t=−526π​

The function y=1.6sin⁡(t−1.8)y = 1.6 \sin ( t - 1.8 )y=1.6sin(t−1.8) 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

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 reference number for $t = - \frac { \pi } { 6 }$

Find the period of the function $y = \frac { 1 } { 3 } \csc 2 x$

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

Find the amplitude, period and phase shift of $y = 2 \cos \left( 4 x - \frac { \pi } { 2 } \right)$ and sketch its graph.

Find the amplitude, period, and phase shift of the function. $y = 2 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 3 } \right)$

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

Find the reference number for $t = - \frac { 22 \pi } { 3 }$ .

Find the reference number for $t = - \frac { 26 \pi } { 5 }$

The function $y = 1.6 \sin ( t - 1.8 )$ 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