Sine and Cosine Graphs

Front

What is the definition of the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough, representing the height of the wave.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The period can be found using the formula: Period = 2π/B, where B is the coefficient of x in the function.

Tags

CCSS.HSF-IF.C.7E

Front

What does the graph of f(x) = 3 sin x look like?

Back

The graph is a sine wave with an amplitude of 3, oscillating between 3 and -3.

Tags

CCSS.HSF-IF.C.7E

Front

How does changing the coefficient of x in f(x) = sin(Bx) affect the graph?

Back

Changing B affects the period of the graph; a larger B results in a shorter period.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The period is 2π/3.

Tags

CCSS.HSF.TF.A.4

Front

What is the amplitude of the function f(x) = -2 cos x?

Back

The amplitude is 2, as amplitude is always a positive value.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine if a function is sine or cosine based on its graph?

Back

A sine graph starts at the midline, while a cosine graph starts at its maximum or minimum value.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of a negative sign in front of a cosine function, such as f(x) = -cos x?

Back

It reflects the graph across the x-axis.

Tags

CCSS.HSF-IF.C.7E

Front

What is the period of the function f(x) = sin(⅓ x)?

Back

The period is 6π.

Tags

CCSS.HSF.TF.A.4

Front

What is the maximum value of the function f(x) = 4 sin x?

Back

The maximum value is 4.

Tags

CCSS.HSF-IF.C.7E