Question 1

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places.
-5

Accepted Answer

A)  -0.08° 
B)  286.48° 
C)  286.23° 
D)  0.09° 
A)  -0.08° 
B)  286.48° 
C)  286.23° 
D)  0.09°

Question 2

Graph the function. Show at least one period.
-$y=-3 \cos (x-\pi)$
 
 A)

Accepted Answer

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

Question 3

Solve the problem.
-For what numbers $x , - 2 \pi \leq x \leq 2 \pi$, does the graph of $y = \csc x$ have vertical asymptotes?

Accepted Answer

A)  $- 2 , - 1,0,1,2$ 
B)  $- \frac { 3 \pi } { 2 } , - \frac { \pi } { 2 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $- 2 \pi , - \pi , 0 , \pi , 2 \pi$ 
D)  none 
A)  $- 2 , - 1,0,1,2$ 
B)  $- \frac { 3 \pi } { 2 } , - \frac { \pi } { 2 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $- 2 \pi , - \pi , 0 , \pi , 2 \pi$ 
D)  none

Question 4

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta = ?$

Accepted Answer

A)  $14.86 ^ { \circ }$ 
B)  $1,560,152.87 ^ { \circ }$ 
C)  $29.72 ^ { \circ }$ 
D)  $780,076.43 ^ { \circ }$ 
A)  $14.86 ^ { \circ }$ 
B)  $1,560,152.87 ^ { \circ }$ 
C)  $29.72 ^ { \circ }$ 
D)  $780,076.43 ^ { \circ }$

Question 5

Solve the problem.
-$$\text { Is the function } f ( \theta ) = \sin \theta + \tan \theta \text { even, odd, or neither? }$$

Accepted Answer

The answer of Solve the problem.
-\[\text { Is the function...

Question 6

Draw the angle.
-$\frac { 5 \pi } { 3 }$

Accepted Answer

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

Question 7

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$$\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)$$
Find $\cos \theta$.

Accepted Answer

A)  $- \frac { 34 } { 5 }$ 
B)  $\frac { 5 \sqrt { 34 } } { 34 }$ 
C)  $- \frac { 3 \sqrt { 34 } } { 34 }$ 
D)  $\frac { 34 } { 3 }$ 
A)  $- \frac { 34 } { 5 }$ 
B)  $\frac { 5 \sqrt { 34 } } { 34 }$ 
C)  $- \frac { 3 \sqrt { 34 } } { 34 }$ 
D)  $\frac { 34 } { 3 }$

Question 8

Find the exact value of the indicated trigonometric function of $\theta$
-$\sin \theta = \frac { 1 } { 2 } , \quad \sec \theta < 0$
Find $\cos \theta$ and $\tan \theta$.

Accepted Answer

A)  $\cos \theta = - \sqrt { 3 } , \tan \theta = - \frac { 10 \sqrt { 3 } } { 3 }$ 
B)  $\cos \theta = - \frac { \sqrt { 3 } } { 2 } , \tan \theta = \frac { \sqrt { 3 } } { 3 }$ 
C)  $\cos \theta = - \frac { \sqrt { 3 } } { 2 } , \tan \theta = - \frac { \sqrt { 3 } } { 3 }$ 
D)  $\cos \theta = \sqrt { \frac { 3 } { 2 } } , \tan \theta = \frac { \sqrt { 3 } } { 3 }$ 
A)  $\cos \theta = - \sqrt { 3 } , \tan \theta = - \frac { 10 \sqrt { 3 } } { 3 }$ 
B)  $\cos \theta = - \frac { \sqrt { 3 } } { 2 } , \tan \theta = \frac { \sqrt { 3 } } { 3 }$ 
C)  $\cos \theta = - \frac { \sqrt { 3 } } { 2 } , \tan \theta = - \frac { \sqrt { 3 } } { 3 }$ 
D)  $\cos \theta = \sqrt { \frac { 3 } { 2 } } , \tan \theta = \frac { \sqrt { 3 } } { 3 }$

Question 9

Find the phase shift of the function.
-$$y = - 2 \cos \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

A)  $- 2$ units up 
B)  -2 units down 
C)  $\frac { \pi } { 4 }$ units to the right 
D)  $\frac { \pi } { 4 }$ units to the left 
A)  $- 2$ units up 
B)  -2 units down 
C)  $\frac { \pi } { 4 }$ units to the right 
D)  $\frac { \pi } { 4 }$ units to the left

Question 10

Match the function to its graph.
-$$y = - \tan \left( x + \frac { \pi } { 2 } \right)$$

Accepted Answer

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

Question 11

Find the exact value of the expression. Do not use a calculator.
-$\tan 150 ^ { \circ } \cos 210 ^ { \circ }$

Accepted Answer

A)  $\frac { 2 \sqrt { 3 } + 3 } { 6 }$ 
B)  $\frac { 3 \sqrt { 3 } + 2 \sqrt { 3 } } { 6 }$ 
C)  $\frac { \sqrt { 3 } + 1 } { 2 }$ 
D)  $- \frac { 5 \sqrt { 3 } } { 6 }$ 
A)  $\frac { 2 \sqrt { 3 } + 3 } { 6 }$ 
B)  $\frac { 3 \sqrt { 3 } + 2 \sqrt { 3 } } { 6 }$ 
C)  $\frac { \sqrt { 3 } + 1 } { 2 }$ 
D)  $- \frac { 5 \sqrt { 3 } } { 6 }$

Question 12

Without graphing the function, determine its amplitude or period as requested.
-$y = - 3 \cos x \quad$ Find the period.

Accepted Answer

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

Question 13

Solve the problem.
-The path of a projectile fired at an inclination $\theta$ to the horizontal with an initial speed vo is a parabola. The range R of the projectile, the horizontal distance that the projectile travels, is found by the formula $\mathrm { R } = \frac { \mathrm { v } _ { \mathrm { O } } ^ { 2 } \sin 2 \theta } { \mathrm { g } }$ where g = 32.2 feet per second per second or g = 9.8 meters per second per second. Find the
Range of a projectile fired with an initial velocity of 174 feet per second at an angle of 35° to the horizontal.
Round your answer to two decimal places.

Accepted Answer

A)  883.54 ft 
B)  883.44 ft 
C)  1,078.61 ft 
D)  539.30 ft 
A)  883.54 ft 
B)  883.44 ft 
C)  1,078.61 ft 
D)  539.30 ft

Question 14

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\cos 72 ^ { \circ }$

Accepted Answer

A)  $0.36$ 
B)  $- 0.92$ 
C)  $- 0.97$ 
D)  $0.31$ 
A)  $0.36$ 
B)  $- 0.92$ 
C)  $- 0.97$ 
D)  $0.31$

Question 15

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\sec \frac { \pi } { 12 }$

Accepted Answer

A)  $1.00$ 
B)  $0.94$ 
C)  $1.04$ 
D)  $0.98$ 
A)  $1.00$ 
B)  $0.94$ 
C)  $1.04$ 
D)  $0.98$

Question 16

Without graphing the function, determine its amplitude or period as requested.
-$y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quad$ Find the period.

Accepted Answer

A)  $\frac { 7 } { 4 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 3 \pi } { 2 }$ 
D)  $\frac { 16 \pi } { 7 }$ 
A)  $\frac { 7 } { 4 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 3 \pi } { 2 }$ 
D)  $\frac { 16 \pi } { 7 }$

Question 17

Graph the function.
-$y=-\cot \left(x-\frac{\pi}{4}\right)$
 
 A)

Accepted Answer

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

Question 18

Use transformations to graph the function.
-$y=2 \sin (\pi-x)$
 
 A)

Accepted Answer

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

Question 19

Find the phase shift of the function.
-$$y = - 3 \cos ( 4 x + \pi )$$

Accepted Answer

A)  $\frac { \pi } { 3 }$ units to the left 
B)  $3 \pi$ units to the right 
C)  $4 \pi$ units to the right 
D)  $\frac { \pi } { 4 }$ units to the left 
A)  $\frac { \pi } { 3 }$ units to the left 
B)  $3 \pi$ units to the right 
C)  $4 \pi$ units to the right 
D)  $\frac { \pi } { 4 }$ units to the left

Question 20

Convert the angle in radians to degrees.
-$$- \frac { 23 } { 9 } \pi$$

Accepted Answer

A)  $- 920 \pi ^ { \circ }$ 
B)  $- 230 ^ { \circ }$ 
C)  $- 8 ^ { \circ }$ 
D)  $- 460 ^ { \circ }$ 
A)  $- 920 \pi ^ { \circ }$ 
B)  $- 230 ^ { \circ }$ 
C)  $- 8 ^ { \circ }$ 
D)  $- 460 ^ { \circ }$

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. -5

Solve the problem. -For what numbers $x , - 2 \pi \leq x \leq 2 \pi$ , does the graph of $y = \csc x$ have vertical asymptotes?

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta = ?$

Solve the problem. - $\text { Is the function } f ( \theta ) = \sin \theta + \tan \theta \text { even, odd, or neither? }$

Draw the angle. - $\frac { 5 \pi } { 3 }$

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)$ Find $\cos \theta$ .

Find the exact value of the indicated trigonometric function of $\theta$ - $\sin \theta = \frac { 1 } { 2 } , \quad \sec \theta < 0$ Find $\cos \theta$ and $\tan \theta$ .

Find the phase shift of the function. - $y = - 2 \cos \left( x + \frac { \pi } { 4 } \right)$

Match the function to its graph. - $y = - \tan \left( x + \frac { \pi } { 2 } \right)$

Find the exact value of the expression. Do not use a calculator. - $\tan 150 ^ { \circ } \cos 210 ^ { \circ }$

Without graphing the function, determine its amplitude or period as requested. - $y = - 3 \cos x \quad$ Find the period.

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 72 ^ { \circ }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sec \frac { \pi } { 12 }$

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quad$ Find the period.

Find the phase shift of the function. - $y = - 3 \cos ( 4 x + \pi )$

Convert the angle in radians to degrees. - $- \frac { 23 } { 9 } \pi$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 5: Trigonometric Functions

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. -5

Graph the function. Show at least one period. - y=−3cos⁡(x−π)y=-3 \cos (x-\pi)y=−3cos(x−π) A) B) C) D)

Solve the problem. -For what numbers x,−2π≤x≤2πx , - 2 \pi \leq x \leq 2 \pix,−2π≤x≤2π , does the graph of y=csc⁡xy = \csc xy=cscx have vertical asymptotes?

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - r=18\mathrm { r } = 18r=18 feet, A=84\mathrm { A } = 84A=84 square feet, θ=?\theta = ?θ=?

Solve the problem. - Is the function f(θ)=sin⁡θ+tan⁡θ even, odd, or neither? \text { Is the function } f ( \theta ) = \sin \theta + \tan \theta \text { even, odd, or neither? } Is the function f(θ)=sinθ+tanθ even, odd, or neither?

Draw the angle. - 5π3\frac { 5 \pi } { 3 }35π​

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - (−15,13)\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)(−51​,31​) Find cos⁡θ\cos \thetacosθ .

Find the exact value of the indicated trigonometric function of θ\thetaθ - sin⁡θ=12,sec⁡θ<0\sin \theta = \frac { 1 } { 2 } , \quad \sec \theta < 0sinθ=21​,secθ<0 Find cos⁡θ\cos \thetacosθ and tan⁡θ\tan \thetatanθ .

Find the phase shift of the function. - y=−2cos⁡(x+π4)y = - 2 \cos \left( x + \frac { \pi } { 4 } \right)y=−2cos(x+4π​)

Match the function to its graph. - y=−tan⁡(x+π2)y = - \tan \left( x + \frac { \pi } { 2 } \right)y=−tan(x+2π​)

Find the exact value of the expression. Do not use a calculator. - tan⁡150∘cos⁡210∘\tan 150 ^ { \circ } \cos 210 ^ { \circ }tan150∘cos210∘

Without graphing the function, determine its amplitude or period as requested. - y=−3cos⁡xy = - 3 \cos x \quady=−3cosx Find the period.

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cos⁡72∘\cos 72 ^ { \circ }cos72∘

Use a calculator to find the approximate value of the expression rounded to two decimal places. - sec⁡π12\sec \frac { \pi } { 12 }sec12π​

Without graphing the function, determine its amplitude or period as requested. - y=76sin⁡(−8π3x)y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quady=67​sin(−38π​x) Find the period.

Graph the function. - y=−cot⁡(x−π4)y=-\cot \left(x-\frac{\pi}{4}\right)y=−cot(x−4π​) A) B) C) D)

Use transformations to graph the function. - y=2sin⁡(π−x)y=2 \sin (\pi-x)y=2sin(π−x) A) B) C) D)

Find the phase shift of the function. - y=−3cos⁡(4x+π)y = - 3 \cos ( 4 x + \pi )y=−3cos(4x+π)

Convert the angle in radians to degrees. - −239π- \frac { 23 } { 9 } \pi−923​π

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Solve the problem. -For what numbers $x , - 2 \pi \leq x \leq 2 \pi$ , does the graph of $y = \csc x$ have vertical asymptotes?

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta = ?$

Solve the problem. - $\text { Is the function } f ( \theta ) = \sin \theta + \tan \theta \text { even, odd, or neither? }$

Draw the angle. - $\frac { 5 \pi } { 3 }$

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)$ Find $\cos \theta$ .

Find the exact value of the indicated trigonometric function of $\theta$ - $\sin \theta = \frac { 1 } { 2 } , \quad \sec \theta < 0$ Find $\cos \theta$ and $\tan \theta$ .

Find the phase shift of the function. - $y = - 2 \cos \left( x + \frac { \pi } { 4 } \right)$

Match the function to its graph. - $y = - \tan \left( x + \frac { \pi } { 2 } \right)$

Find the exact value of the expression. Do not use a calculator. - $\tan 150 ^ { \circ } \cos 210 ^ { \circ }$

Without graphing the function, determine its amplitude or period as requested. - $y = - 3 \cos x \quad$ Find the period.

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 72 ^ { \circ }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sec \frac { \pi } { 12 }$

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 7 } { 6 } \sin \left( - \frac { 8 \pi } { 3 } x \right) \quad$ Find the period.

Find the phase shift of the function. - $y = - 3 \cos ( 4 x + \pi )$

Convert the angle in radians to degrees. - $- \frac { 23 } { 9 } \pi$