Graphing Trig Functions

Front

What is the general form of a sine function?

Back

y = a sin(bx - c) + d, where: - a = amplitude - b = frequency - c = phase shift - d = vertical shift

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of a cosine function?

Back

y = a cos(bx - c) + d, where: - a = amplitude - b = frequency - c = phase shift - d = vertical shift

Tags

CCSS.HSF-IF.C.7E

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is given by the absolute value of 'a' in the function y = a sin(bx - c) + d.

Tags

CCSS.HSF-IF.C.7E

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the function. It is calculated as 2π/b, where b is the coefficient of x.

Tags

CCSS.HSF.TF.A.4

Front

What is the phase shift of a trigonometric function?

Back

The phase shift is the horizontal shift left or right for the graph of the function. It is calculated as c/b in the function y = a sin(bx - c) + d.

Tags

CCSS.HSF-IF.C.7E

Front

What is the vertical shift of a trigonometric function?

Back

The vertical shift is the amount the graph is moved up or down. It is represented by 'd' in the function y = a sin(bx - c) + d.

Tags

CCSS.HSF-IF.C.7E

Front

What is the domain of the sine function?

Back

The domain of y = sin(x) is all real numbers: (-∞, ∞).

Front

What is the range of the sine function?

Back

The range of y = sin(x) is [-1, 1].

Tags

CCSS.HSF.TF.A.4

Front

What is the domain of the cosine function?

Back

The domain of y = cos(x) is all real numbers: (-∞, ∞).

Front

What is the range of the cosine function?

Back

The range of y = cos(x) is [-1, 1].

Tags

CCSS.HSF.TF.A.4