Trig Graphs & Transformations

Front

What is the general form of a sine function?

Back

The general form of a sine function 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 does the amplitude of a trigonometric function represent?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the period of a sine or cosine function?

Back

The period of a sine or cosine function is determined by the formula: Period = (2π)/|b|, where 'b' is the coefficient of x in the function.

Tags

CCSS.HSF.TF.A.4

Front

What is a vertical shift in a trigonometric function?

Back

A vertical shift is represented by 'd' in the function y = a*sin(bx - c) + d. It moves the graph up or down on the y-axis.

Tags

CCSS.HSF-IF.C.7E

Front

What is the equation of a cosine function with amplitude 2, period 2π, and vertical shift 3?

Back

Tags

CCSS.HSF-IF.C.7E

Front

What is the phase shift in the function y = a*sin(bx - c) + d?

Back

The phase shift is given by c/b. It indicates how much the graph is shifted horizontally.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between sine and cosine functions?

Back

Sine functions start at the midline (0) and go up, while cosine functions start at the maximum value (amplitude) and go down.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify the vertical shift in the function y = a*sin(bx - c) + d?

Back

The vertical shift is represented by 'd'. It indicates how far the graph is moved up or down from the origin.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of changing 'b' in the function y = a*sin(bx)?

Back

Changing 'b' affects the period of the function. A larger 'b' results in a shorter period, while a smaller 'b' results in a longer period.

Tags

CCSS.HSF-IF.C.7E

Front

What is the equation for a sine function with an amplitude of 4, period π, and no vertical shift?

Back

Tags

CCSS.HSF-IF.C.7E