Graphing Sin & Cos

Front

What is the amplitude of a sine function?

Back

The amplitude of a sine function is the maximum distance from the midline (equilibrium position) of the graph to its peak or trough.

Front

What effect does changing the coefficient in front of sin(x) have on the graph?

Back

Changing the coefficient in front of sin(x) affects the amplitude of the graph. For example, y = 4sin(x) has an amplitude of 4.

Front

What is the period of the function y = sin(kx)?

Back

The period of the function y = sin(kx) is given by the formula: Period = 2π/k.

Front

How does the graph of y = sin(x) differ from y = sin(2x)?

Back

The graph of y = sin(2x) has a shorter period than y = sin(x). Specifically, the period of y = sin(2x) is π.

Front

What is a phase shift in trigonometric functions?

Back

A phase shift is a horizontal shift left or right for the graph of a function. It occurs when the function is in the form y = sin(x - c) or y = cos(x - c).

Front

What is the amplitude of y = 3cos(x)?

Back

The amplitude of y = 3cos(x) is 3.

Front

What happens to the graph of y = sin(x) when you multiply x by a factor greater than 1?

Back

Multiplying x by a factor greater than 1 compresses the graph horizontally, resulting in a shorter period.

Front

What is the difference between y = sin(x) and y = sin(x + π)?

Back

The graph of y = sin(x + π) is a phase shift of π units to the left compared to y = sin(x).

Front

What is the vertical shift in the function y = sin(x) + 2?

Back

The vertical shift of the function y = sin(x) + 2 is 2 units upward.

Front

How do you determine the maximum and minimum values of y = 5sin(x)?

Back

The maximum value is 5 and the minimum value is -5, determined by the amplitude.