Unit 5, Quiz 2 Review

Unit 5, Quiz 2 Review

You have an unlimited number of attempts to complete this review and practice for your quiz tomorrow.
The highest score will count towards your grade on AERIES.

Unit Circle

Match

Match the following trigonometric functions with their definition on the Unit Circle.

• $$\sin\theta$$

• $$\cos\theta$$

• $$\tan\theta$$

• $$y$$

• $$x$$

• $$\frac{y}{x}$$

Multiple Choice

What is $$\sin120\degree?$$

• $$\frac{\sqrt[]{3}}{2}$$

• $$\frac{1}{2}$$

• $$\frac{\sqrt[]{2}}{2}$$

• $$-\frac{\sqrt[]{3}}{2}$$

Multiple Choice

What is $$\sin\pi$$ ?

• $$1$$

• $$-1$$

• $$0$$

• $$180\degree$$

Multiple Choice

What is $$\sin\frac{3\pi}{2}$$ ?

• $$1$$

• $$-1$$

• $$0$$

• $$\frac{\sqrt[]{2}}{2}$$

Multiple Choice

What is $$\cos225\degree$$ ?

• $$\frac{\sqrt[]{2}}{2}$$

• $$\frac{5\pi}{4}$$

• $$-\frac{\sqrt[]{2}}{2}$$

• $$\frac{\sqrt[]{3}}{2}$$

Multiple Choice

What is $$\cos\frac{\pi}{2}$$ ?

• $$0$$

• $$1$$

• $$-1$$

• $$90\degree$$

Multiple Choice

What is $$\cos\frac{\pi}{3}$$ ?

• $$\frac{\sqrt[]{2}}{2}$$

• $$\frac{1}{2}$$

• $$\frac{\sqrt[]{3}}{2}$$

• $$-\frac{1}{2}$$

Sine and Cosine Functions

The amplitude of a sine or cosine function is the height of the wave.

• ​We can find the amplitude by measuring the distance from the midline to the peak of the wave.

• We can also find the distance from the max to the min and divide it in half to get the amplitude.

Amplitude

Multiple Choice

What is the amplitude?

• $$2$$

• $$4$$

• $$8$$

• $$-6$$

Multiple Choice

What is the amplitude of the graph?

• $$1$$

• $$2$$

• $$6$$

• $$4$$

Multiple Choice

What is the amplitude of the graph? 

• $$5$$

• $$4$$

• $$2$$

• $$2.5$$

The period of a sine or cosine function is the wavelength.

• It is how far we go on the graph before it starts repeating itself.

• On a graph, the period goes from one peak to the next (or from any point to the next matching point).

​

​Period

Multiple Choice

What is the period of the graph?

• $$\pi$$

• $$2\pi$$

• $$3\pi$$

• $$4\pi$$

Multiple Choice

What is the period of the graph?

• $$\pi$$

• $$\frac{\pi}{2}$$

• $$2\pi$$

• $$4\pi$$

Multiple Choice

What is the period of the graph? 

• $$2\pi$$

• $$4\pi$$

• $$\pi$$

• $$\frac{3\pi}{2}$$

Multiple Choice

What is the period of this graph?

• $$2\pi$$

• $$\frac{\pi}{2}$$

• $$\frac{\pi}{4}$$

• $$\pi$$

The midline is the horizontal line that cuts the graph in half.

The midline is also known as the vertical shift of the sine or cosine function.

​

​Midline (Vertical Shift)

Multiple Choice

What is the midline (vertical shift)?

• $$2$$

• $$4$$

• $$-2$$

• $$-6$$

Multiple Choice

What is the midline (vertical shift)?

• $$1$$

• $$2$$

• $$3$$

• $$4$$

Multiple Choice

What is the midline (vertical shift)?

• $$2$$

• $$-1$$

• $$3$$

• $$-4$$

Transformations of Sine and Cosine

Multiple Choice

Which value represents a horizontal shift (left and right) in the following function $$y=A\sin\left(B\left(x-h\right)\right)+k$$ ?

• A

• B

• h

• k

Multiple Choice

Which value represents a vertical shift (up and down) in the following function $$y=A\sin\left(B\left(x-h\right)\right)+k$$ ?

• A

• B

• h

• k

Multiple Select

Describe the transformation:
$$f\left(x\right)\ =\ \cos\left(x\ -\ \frac{\pi}{4}\right)$$  

• Up  $$\frac{\pi}{4}$$  

• Down $$\frac{\pi}{4}$$

• Left  $$\frac{\pi}{4}$$  

• Right  $$\frac{\pi}{4}$$  

Multiple Choice

What is the horizontal shift?
$$y\ =\ 4\cos2\left(x\ +\frac{\pi}{2}\right)-2$$  

• left $$\frac{\pi}{2}$$  

• right $$\frac{\pi}{2}$$

• right  $$\pi$$  

• left  $$\pi$$  

Multiple Choice

What is the vertical shift (midline) for
$$y=4\cos\ \frac{1}{2}\left(x+\pi\right)-2$$ ?

• $$y=2$$

• $$y=-2$$

• $$y=4$$

• $$y=-4$$

Multiple Choice

What is the amplitude?
$$y\ =\ 3\sin7\left(x\ +\ \pi\right)\ -\ 2$$

• 7

• -2

• 3

• 6

Multiple Choice

Which of the following is the formula to find the period of a sine or cosine function?

• $$Period=\frac{2\pi}{B}$$

• $$Period=\frac{B}{2\pi}$$

• $$Period=\frac{\pi}{B}$$

• $$Period=2\pi\cdot B$$

Multiple Choice

What is the period?
$$y\ =\ 3\sin7\left(x\ +\ \pi\right)\ -\ 2$$

• 7

• $$7\pi$$

• $$\frac{2\pi}{7}$$

• $$14\pi$$

Multiple Choice

What is the period of the function?
$$y\ =\ 3\cos5\left(x\right)$$  

• $$10\pi$$

• $$\frac{2\pi}{5}$$  
  

• $$\frac{1}{5}$$  

• 10

Multiple Choice

What is the period for
$$y=4\cos2\left(x+\pi\right)-2$$ ?

• $$4\pi$$

• $$\pi$$

• $$\frac{\pi}{2}$$

• $$2\pi$$

Sine and Cosine graphs look identical, but we can tell them apart by looking at their y-intercepts.

​Sine Graphs
y -intercept = midline

Cosine Graphs
y-intercept = max or min

Sine vs. Cosine Graphs

Multiple Choice

Sine or Cosine?

• $$y=\sin x$$

• $$y=\cos x$$

Multiple Choice

Sine or Cosine?

• $$y=\sin x$$

• $$y=\cos x$$

Multiple Choice

What is the equation of the graph?

• $$y=2\cos x$$

• $$y=\sin x$$

• $$y=2\sin x$$

• $$y=\sin2x$$

Multiple Choice

What is the equation of graph? 

• $$y=\sin5x$$

• $$y=\cos5x$$

• $$y=5\sin x$$

• $$y=5\cos x$$

Remember your quiz is tomorrow and will cover the last 3 sections of Unit 5 (Guided Notes #4 - 6).