Sine and Cosine - Amplitude and Period

Front

What is the formula to find the period of a sine or cosine graph?

Back

Tags

CCSS.HSF-IF.C.7E

Front

What is the period of the function y = -3sin(x)?

Back

The period of y = -3sin(x) is 2π.

Tags

CCSS.HSF.TF.A.4

Front

Define 'period' in the context of sine and cosine graphs.

Back

The period is the horizontal length required to complete one full cycle of the graph.

Tags

CCSS.HSF.TF.A.4

Front

What is the amplitude of a sine or cosine graph?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph.

Tags

CCSS.HSF-IF.C.7E

Front

What is the amplitude of the graph y = -3sin(x)?

Back

The amplitude is 3.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of a sine function?

Back

The general form is y = a sin(bx + c) + d, where a is the amplitude, b affects the period, c is the phase shift, and d is the vertical shift.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of a cosine function?

Back

The general form is y = a cos(bx + c) + d, where a is the amplitude, b affects the period, c is the phase shift, and d is the vertical shift.

Tags

CCSS.HSF-IF.C.7E

Front

How does the value of 'b' affect the period of the sine and cosine functions?

Back

Tags

CCSS.HSF-IF.C.7E

Front

What happens to the graph of y = sin(x) when the amplitude is increased?

Back

Increasing the amplitude stretches the graph vertically, making the peaks and troughs further from the midline.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of a negative amplitude in a sine or cosine function?

Back

A negative amplitude reflects the graph across the midline.

Tags

CCSS.HSF-IF.C.7E