Question 1

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)  $\sin ( t ) = - \frac { 5 } { 13 }$, $\cos ( t ) = \frac { 12 } { 13 }$, $\tan t = \frac { 12 } { 5 }$ B

Question 2

Find the approximate value of $\cos ( - 1.1 )$ using a calculator

Accepted Answer

A)  $- 0.02$ 
B)  $0.99$ 
C)  $0.45$ 
D)  $0.89$ 
A)  $- 0.02$ 
B)  $0.99$ 
C)  $0.45$ 
D)  $0.89$ C

Question 3

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

Accepted Answer

$\frac { \pi } { 5 }$

Question 4

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

Accepted Answer

A)  $\tan t = - \frac { 3 } { 4 }$ 
B)  $\tan t = - \frac { 3 } { 5 }$ 
C)  $\tan t = - 1$ 
D)  $\tan t = \frac { 3 } { 4 }$ 
E)  $\tan t = - \frac { \sqrt { 3 } } { 2 }$ 
A)  $\tan t = - \frac { 3 } { 4 }$ 
B)  $\tan t = - \frac { 3 } { 5 }$ 
C)  $\tan t = - 1$ 
D)  $\tan t = \frac { 3 } { 4 }$ 
E)  $\tan t = - \frac { \sqrt { 3 } } { 2 }$

Question 5

Find the period of the function $y = ( \cot x ) / 5$  and sketch its graph.

Accepted Answer

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

Question 6

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

Accepted Answer

Amplitude

Question 7

Find the exact value of $\sin \left( \frac { 5 \pi } { 2 } \right)$ and $\text {cos} \left( - \frac { 5 \pi } { 2 } \right)$

Accepted Answer

A)  $\sin \left( \frac { 5 \pi } { 2 } \right) = \frac { 5 } { 2 }$, $\mathrm { cos } \left( - \frac { 5 \pi } { 2 } \right) = \frac { 3 } { 2 }$ 
B)  $\sin \left( \frac { 5 \pi } { 2 } \right) = - 1$, $\cos \left( - \frac { 5 \pi } { 2 } \right) = 0$ 
C)  $\sin \left( \frac { 5 \pi } { 2 } \right) = 0$, $\cos \left( - \frac { 5 \pi } { 2 } \right) = - 1$ 
D)  $\sin \left( \frac { 5 \pi } { 2 } \right) = 1$, $\cos \left( - \frac { 5 \pi } { 2 } \right) = 0$ 
E)  $\sin \left( \frac { 5 \pi } { 2 } \right) = - 1$, $cos \left( - \frac { 5 \pi } { 2 } \right) = 1$ 
A)  $\sin \left( \frac { 5 \pi } { 2 } \right) = \frac { 5 } { 2 }$, $\mathrm { cos } \left( - \frac { 5 \pi } { 2 } \right) = \frac { 3 } { 2 }$ 
B)  $\sin \left( \frac { 5 \pi } { 2 } \right) = - 1$, $\cos \left( - \frac { 5 \pi } { 2 } \right) = 0$ 
C)  $\sin \left( \frac { 5 \pi } { 2 } \right) = 0$, $\cos \left( - \frac { 5 \pi } { 2 } \right) = - 1$ 
D)  $\sin \left( \frac { 5 \pi } { 2 } \right) = 1$, $\cos \left( - \frac { 5 \pi } { 2 } \right) = 0$ 
E)  $\sin \left( \frac { 5 \pi } { 2 } \right) = - 1$, $cos \left( - \frac { 5 \pi } { 2 } \right) = 1$

Question 8

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 9

Find to two decimal places the value of $\cos ( - 6.1 )$ 
using a calculator.

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $2 \pi$ 
B)  $\pi$ 
C)  $3 \pi$ 
D)  $\pi / 3$ 
E)  $2 \pi / 3$ 
A)  $2 \pi$ 
B)  $\pi$ 
C)  $3 \pi$ 
D)  $\pi / 3$ 
E)  $2 \pi / 3$

Question 12

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

The answer of The function \(y = 1.6 \sin (...

Question 13

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 14

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

Accepted Answer

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

Question 15

Find the amplitude, period and phase shift of $y = - \frac { 5 } { 4 } \cos \left( 2 x - \frac { 4 \pi } { 3 } \right)$

Accepted Answer

A) amplitude: $\frac { 5 } { 4 }$, period: $\pi$, phase shift: $\frac { 2 \pi } { 3 }$To the left 
B) amplitude: $\frac { 5 } { 4 }$, period: $2 \pi$, phase shift: $\frac { 4 \pi } { 3 }$To the right 
C) amplitude: $- \frac { 5 } { 4 }$, period: $\pi$, phase shift: $\frac { 5 \pi } { 3 }$To the left 
D) amplitude: $- \frac { 5 } { 4 }$, period: $2 \pi$, phase shift: $\frac { 2 \pi } { 3 }$To the right 
E)  amplitude: $\frac { 5 } { 4 }$, period: $\pi$, phase shift: $\frac { 2 \pi } { 3 }$To the right 
A) amplitude: $\frac { 5 } { 4 }$, period: $\pi$, phase shift: $\frac { 2 \pi } { 3 }$To the left 
B) amplitude: $\frac { 5 } { 4 }$, period: $2 \pi$, phase shift: $\frac { 4 \pi } { 3 }$To the right 
C) amplitude: $- \frac { 5 } { 4 }$, period: $\pi$, phase shift: $\frac { 5 \pi } { 3 }$To the left 
D) amplitude: $- \frac { 5 } { 4 }$, period: $2 \pi$, phase shift: $\frac { 2 \pi } { 3 }$To the right 
E)  amplitude: $\frac { 5 } { 4 }$, period: $\pi$, phase shift: $\frac { 2 \pi } { 3 }$To the right

Question 16

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

Accepted Answer

A)  $x = \sqrt { 11 } , 6$ 
B)  $x = - \sqrt { 11 } / 6$ 
C)  $x = 11 / 6$ 
D)  $x = - 11 / 6$ 
E) none of these 
A)  $x = \sqrt { 11 } , 6$ 
B)  $x = - \sqrt { 11 } / 6$ 
C)  $x = 11 / 6$ 
D)  $x = - 11 / 6$ 
E) none of these

Question 17

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 18

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

Accepted Answer

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

Question 19

Find the exact value of $\operatorname { sit } \left( \frac { 9 x } { 2 } \right)$ and $\operatorname { Cos} \left( - \frac { 9 x } { 2 } \right)$ .

Accepted Answer

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

Question 20

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...

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 approximate value of $\cos ( - 1.1 )$ using a calculator

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

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

Find the period of the function $y = ( \cot x ) / 5$ 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 $\sin \left( \frac { 5 \pi } { 2 } \right)$ and $\text {cos} \left( - \frac { 5 \pi } { 2 } \right)$

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

Find to two decimal places the value of $\cos ( - 6.1 )$ using a calculator.

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

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

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.

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

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

Find the amplitude, period and phase shift of $y = - \frac { 5 } { 4 } \cos \left( 2 x - \frac { 4 \pi } { 3 } \right)$

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

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

Find the exact value of $\operatorname { sit } \left( \frac { 9 x } { 2 } \right)$ and $\operatorname { Cos} \left( - \frac { 9 x } { 2 } \right)$ .

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

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

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 approximate value of cos⁡(−1.1)\cos ( - 1.1 )cos(−1.1) using a calculator

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

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 period of the function y=(cot⁡x)/5y = ( \cot x ) / 5y=(cotx)/5 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 sin⁡(5π2)\sin \left( \frac { 5 \pi } { 2 } \right)sin(25π​) and cos(−5π2)\text {cos} \left( - \frac { 5 \pi } { 2 } \right)cos(−25π​)

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

Find to two decimal places the value of cos⁡(−6.1)\cos ( - 6.1 )cos(−6.1) using a calculator.

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

Find the period of the function y=3sec⁡xy = 3 \sec xy=3secx

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.

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

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

Find the amplitude, period and phase shift of y=−54cos⁡(2x−4π3)y = - \frac { 5 } { 4 } \cos \left( 2 x - \frac { 4 \pi } { 3 } \right)y=−45​cos(2x−34π​)

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

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

Find the exact value of sit⁡(9x2)\operatorname { sit } \left( \frac { 9 x } { 2 } \right)sit(29x​) and Cos⁡(−9x2)\operatorname { Cos} \left( - \frac { 9 x } { 2 } \right)Cos(−29x​) .

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​} .

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

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 approximate value of $\cos ( - 1.1 )$ using a calculator

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

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

Find the period of the function $y = ( \cot x ) / 5$ 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 $\sin \left( \frac { 5 \pi } { 2 } \right)$ and $\text {cos} \left( - \frac { 5 \pi } { 2 } \right)$

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

Find to two decimal places the value of $\cos ( - 6.1 )$ using a calculator.

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

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

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.

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

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

Find the amplitude, period and phase shift of $y = - \frac { 5 } { 4 } \cos \left( 2 x - \frac { 4 \pi } { 3 } \right)$

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

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

Find the exact value of $\operatorname { sit } \left( \frac { 9 x } { 2 } \right)$ and $\operatorname { Cos} \left( - \frac { 9 x } { 2 } \right)$ .

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