Quiz about Graphing Sine & Cosine

Question 1

What are the five critical values for the sine and cosine parent functions?

Accepted Answer

$$0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2},\ 2\pi$$

Answer

$$0,\ \frac{\pi}{6},\ \frac{\pi}{4},\ \frac{\pi}{3},\ \frac{\pi}{2}$$

Answer

$$0,\ \pi,\ 2\pi,\ 3\pi,\ 4\pi$$

Answer

$$0,\ \frac{\pi}{4},\ \frac{\pi}{2},\ \frac{3\pi}{4},\ \pi$$

Question 2

What effect does |a| have on the parent graph?

$$y=a\sin\left(b\left(x-h\right)\right)+k$$

Accepted Answer

Vertical stretch/shrink

Answer

Vertical shift

Answer

Reflect over x-axis

Answer

None

Question 3

Which characteristic does |a| affect?

$$y=a\sin\left(b\left(x-h\right)\right)+k$$

Accepted Answer

Amplitude

Answer

Midline

Answer

Period

Answer

None

Question 4

What effect does a being negative have on the parent graph?

$$y=a\sin\left(b\left(x-h\right)\right)+k$$

Accepted Answer

Reflect over x-axis

Answer

Vertical stretch/shrink

Answer

Vertical shift

Answer

None

Question 5

Which characteristic is affected if a is negative?

$$y=a\sin\left(b\left(x-h\right)\right)+k$$

Accepted Answer

None

Answer

Midline

Answer

Amplitude

Answer

Period

Question 6

What effect does k have on the parent graph?

$$y=a\sin\left(b\left(x-h\right)\right)+k$$

Accepted Answer

Vertical shift

Answer

Vertical stretch/shrink

Answer

Reflect over x-axis

Answer

None

Question 7

Which characteristic does k affect?

$$y=a\sin\left(b\left(x-h\right)\right)+k$$

Accepted Answer

Midline

Answer

Amplitude

Answer

Period

Answer

None

Question 8

Identify the shape of the graph: $$y=\frac{1}{2}\cos x-3$$

Accepted Answer

Question 9

Identify the shape of the graph: $$y=-\sin x+2$$

Accepted Answer

Question 10

Identify the shape of the graph: $$y=-3\cos x$$

Accepted Answer

Question 11

Identify the shape of the graph: $$y=2\sin x-\frac{1}{2}$$

Accepted Answer

Graphing Sine & Cosine

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