Phase and Vertical Shifts of Trig Graphs

Front

What is a vertical shift in a trigonometric function?

Back

A vertical shift refers to the upward or downward movement of the graph of a trigonometric function. It is determined by the constant added or subtracted from the function.

Front

How does a positive vertical shift affect the graph of a function?

Back

A positive vertical shift moves the graph upward by the specified amount.

Front

How does a negative vertical shift affect the graph of a function?

Back

A negative vertical shift moves the graph downward by the specified amount.

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, calculated as half the distance between the maximum and minimum values.

Front

What is the period of a trigonometric function?

Back

The period is the length of one complete cycle of the graph, determined by the coefficient of the variable inside the function.

Front

How do you determine the phase shift of a trigonometric function?

Back

The phase shift is determined by the horizontal translation of the graph, calculated from the equation in the form y = a sin(b(x - c)) or y = a cos(b(x - c)), where c is the phase shift.

Front

What is the general form of a cosine function?

Back

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

Front

What is the effect of changing the value of 'a' in the cosine function y = a cos(x)?

Back

Changing 'a' affects the amplitude of the graph; a larger 'a' results in a taller graph, while a smaller 'a' results in a shorter graph.

Front

What does the value of 'b' represent in the function y = a cos(b(x - c))?

Back

The value of 'b' affects the period of the function, calculated as Period = (2π)/|b|.

Front

If a function has a phase shift of π to the left, how is it represented in the equation?

Back

It is represented as y = a cos(b(x + π)) or y = a sin(b(x + π)).