Graphs of Sin and Cos

Front

What is the period of a sine or cosine function?

Back

The period is the length of one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the wave to its peak or trough. It is half the distance between the maximum and minimum values.

Front

What is the domain of the function y=sin(x)?

Back

D: (-∞, ∞) - The sine function is defined for all real numbers.

Front

What is the range of the function y=sin(x)?

Back

R: [-1, 1] - The sine function outputs values between -1 and 1.

Front

What is the period of y = 4Cos(2x)?

Back

The period is π. The period can be calculated using the formula: Period = 2π / |b|, where b is the coefficient of x.

Front

What is the amplitude of y = 3sin(7x) - 2?

Back

The amplitude is 3. The amplitude is the coefficient of the sine function.

Front

How does a vertical shift affect the graph of a sine or cosine function?

Back

A vertical shift moves the graph up or down without changing its shape or period.

Front

What is the effect of changing the coefficient of x in y = sin(kx)?

Back

Changing the coefficient k affects the period of the function. The new period is 2π / |k|.

Front

What is the difference between sine and cosine functions?

Back

Sine starts at 0 and goes up, while cosine starts at its maximum value (1) and goes down.

Front

What is the phase shift of y = sin(x - π/2)?

Back

The phase shift is π/2 to the right. It shifts the graph horizontally.