Spaghetti Graphs Questions

Trigonometric functions are PERIODIC functions, meaning their graphs repeat themselves over and over every time one period passes.

What is one period of the sine function? (How long does it take to complete one wave?)

• $\pi$

• $2\pi$

• $-1$

• $1$

Trigonometric functions are PERIODIC functions, meaning their graphs repeat themselves over and over every time one period passes.

What is one period of the cosine function? (How long does it take to complete one wave?)

• $\pi$

• $2\pi$

• $-1$

• $1$

Amplitude means the distance from the midline to the maximum or the midline to the minimum. In other words, it's half the distance from the max to the min value of the periodic graph.

What is the amplitude of both sine and cosine?

• 1

• 2

• $2\pi$

• $\pi$

Amplitude means the distance from the midline to the maximum or the midline to the minimum. In other words, it's half the distance from the max to the min value of the periodic graph.

Write down a formula that could help you find the amplitude for any graph. (It doesn't have to be "the" formula - just a formula that you could use for yourself!)

 Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions.

What does letter A do in the equation below?

 $y=A\sin\left(B\left(x-h\right)\right)+k$ 

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

 Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions.

What does letter h do in the equation below?

 $y=A\sin\left(B\left(x-h\right)\right)+k$ 

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

 Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions.

What does letter B do in the equation below?

 $y=A\sin\left(B\left(x-h\right)\right)+k$ 

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

 Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions.

What does letter k do in the equation below?

 $y=A\sin\left(B\left(x-h\right)\right)+k$ 

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

Recall one more transformation: reflections.

How would the graph of  $y=-2\sin x$ compare to the graph of  $y=2\sin x$ ?

• It would be twice as tall

• It would have half the period

• It would be reflected over the x axis

• It would be reflected over the y-axis

How would the graph of  $y=2\sin x$ compare to the graph of  $y=\sin x$ ?

• It would be twice as tall (double the amplitude)

• It would have half the period

• It would be reflected over the x axis

• It would be reflected over the y-axis