Radians and Degrees Review

Unit 1 Assessment Review

Chapter 4 Sections 1, 2, 4, 5, and 6

Section 4.1 - Radian and Degree Measure

• Convert angles from degrees to radians

• Find measures of coterminal angles

• Draw angles in standard position and determine the quadrant in which the terminal side lies

Multiple Select

Determine which angles are coterminal with

$$-\frac{2\pi}{15}$$ (select all that apply) 

• $$\frac{13\pi}{15}$$  

• $$\frac{28\pi}{15}$$  

• $$\frac{43\pi}{15}$$  

• $$-\frac{32\pi}{15}$$  

Multiple Choice

What is 7π/4 radians in degrees?

• 300

• 135

• 315

• 45

Multiple Choice

Which quadrant is -5π/6 in?

• I

• II

• III

• IV

Multiple Choice

Convert 100⁰ to radians

• 5π/9
• π/2
• 5π/8
• 5π/6

Section 4.4 - Trigonometric Functions of Any Angle

• Find exact values of six trigonometric functions given a point

• Find exact values of six trigonometric functions given a function value and a constraint

Multiple Choice

Name the quadrant in which ∠A lies, if tanA < 0, cosA < 0

• 4

• 3

• 2

• 1

Multiple Choice

Name the quadrant in which ∠A lies, if cosA > 0, sinA < 0

• 1

• 2

• 3

• 4

Multiple Choice

Find  $$\sin\left(\theta\right)$$  given that  $$\cot\left(\theta\right)=-\frac{\sqrt{2}}{5}$$  and  $$\cos\left(\theta\right)>0$$ .  

• $$-\frac{5\sqrt{3}}{9}$$  

• $$\frac{\sqrt{6}}{3}$$  

• $$\frac{5\sqrt{2}}{2}$$  

• $$-\frac{5}{9}$$  

Multiple Choice

Find  $$\tan\left(\theta\right)$$  given that  $$\sin\left(\theta\right)=-\frac{3}{5}$$  and  $$\cos\left(\theta\right)>0$$ .  

• $$-\frac{3}{4}$$  

• $$\frac{4}{5}$$  

• $$\frac{4}{3}$$  

• $$-\frac{5}{3}$$  

Multiple Choice

Find cos(θ) given that the terminal side of θ contains the point $$\left(-9,\ 6\right)$$ .

• $$-\frac{3\sqrt{13}}{13}$$

• $$-\frac{\sqrt{13}}{3}$$

• $$\frac{3}{2}$$

• $$\frac{\sqrt{13}}{3}$$

Multiple Choice

Find sec(θ) given that the terminal side of θ contains the point $$\left(\sqrt{5},2\right)$$  .

• $$\frac{3\sqrt{5}}{5}$$

• $$\frac{3}{2}$$

• $$\frac{\sqrt{5}}{2}$$

• $$-\frac{\sqrt{5}}{3}$$

Sections 4.2 and 4.4: Unit Circle and Reference Angles

• Use the Unit Circle to Evaluate trigonometric functions

• Find the measures of reference angles

• Use reference angles to evaluate trigonometric functions

Multiple Choice

What is the exact value?

$$\cos\left(-\frac{13\pi}{6}\right)$$  

• -1 / 2

• √3 / 2

• -√3 / 2

• 1 / 2

Multiple Choice

What is the reference angle for

$$\frac{2\pi}{3}$$  

• pi/4

• 7pi/6

• 4pi/3

• pi/3

Multiple Choice

What is the reference angle for 63°?

• 117°

• 207°

• 63°

• 153°

Multiple Choice

What is the exact value of $$\sin\left(-660\degree\right)$$  ?

• $$\frac{\sqrt{3}}{2}$$

• 1/2

• -1/2

• 1

Multiple Choice

What is the $$\cos\left(585\degree\right)$$  ?

• $$\frac{1}{2}$$

• $$\frac{\sqrt{2}}{2}$$

  
  

• $$-\frac{\sqrt{2}}{2}$$

• $$-\frac{\sqrt{3}}{2}$$

Multiple Choice

What is the reference angle for -310⁰?

• 50⁰

• -50⁰

• 20⁰

• 40⁰

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°

Multiple Choice

Find the exact value of tan (-π)

• undefined

• 0

• 1

• -1

Multiple Choice

Find the exact value of sec 3π/2

• 0

• undefined

• 1

• -1

Multiple Choice

Find the exact value of

$$\cos\left(\frac{5\pi}{6}\right)$$  

• -√3/2

• -½

• -√2/2

• -1

Multiple Choice

What are the exact coordinates of 3π/4 on the unit circle?

• (−√2∕2, √2∕2)

• (−√2∕2, −√2∕2)

• (−√3∕2, −√2∕2)

• (√2∕2, −√2∕2)

Multiple Choice

Find the exact value of sin (2π/3)

• 1/2

• -1/2

• √3/2

• -√3/2

Multiple Choice

Find the exact value of cos (5π/6)

• -1/2

• 1/2

• √3/2

• -√3/2

Section 4.5: Graphs of Sine and Cosine

• Graph transformations of sine and cosine

• Write equations of sinusoids given a graph

• Write equation of sinusoid to model a real life situation

Multiple Choice

Which of the following is the table of values for

$$y=3\sin2\left(x+\pi\right)+2$$  

Multiple Choice

what is the amplitude of
y = 3sin (7x) -2

• 7
• -2
• 3
• 6

Multiple Choice

What is the period of y=4cos5x

• 2π/5
• π
• 5
• 5π

Multiple Choice

Which of the following is the table of values for

$$y=-2\cos\frac{\pi}{4}\left(x-2\right)+3$$  

Multiple Choice

Write the equation for a sine function with an amplitude of 6 and a period of π/4 and no phase shift.

• y=6sin(8x)

• y=6sin8(x-1)

• y=6sin1/4x

• y=6sinx

Multiple Choice

What is the period?

• $$\frac{\pi}{2}$$

• $$\pi$$

• $$\frac{3\pi}{2}$$

• $$2\pi$$

Multiple Choice

What is the the amplitude of the graphed function?

• 5
• 4
• 3
• 2

Multiple Choice

A weight attached to the end of a long spring is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time. You start a stopwatch. When the stopwatch reads 0.3 seconds, the weight first reaches a high point 60 cm above the floor. The next low point, 40 cm above the floor, occurs at 1.8 seconds. Write a cosine model to represent the height of the weight as a function of time.

• $$y=10\cos3x+50$$

• $$y=10\cos3(x-0.3)+50$$

• $$y=10\cos\frac{2\pi}{3}\left(x-0.3\right)+50$$

• $$y=-10\cos\frac{2\pi}{3}\left(x-0.3\right)+50$$

​4.6 Graphs of Tangent Functions

• ​Identify period and vertical asymptotes of tangent functions

• ​Sketch graphs of tangent functions

Multiple Select

How do you find the period of a tangent function?

• 270/b

• π/b

• 360/b

• 2π/b

Multiple Choice

What is the period of y=4tan5x

• π/5

• π

• 5

• 5π

• 2π/5

Multiple Choice

What function is graphed here?

• sine

• cosine

• tangent

• not listed here

Multiple Choice

Which is a vertical asymptote of:  $$f\left(\theta\right)=\frac{1}{3}\tan\left(\frac{3}{4}\theta\right)$$  

• x = 3π/4

• x = 0

• x = 4π/3

• x = 2π/3