Sin and Cos Graphs

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum value of the function, which is the distance from the midline to the peak. For example, in the function y = 3sin(x), the amplitude is 3.

Front

What is the period of the sine and cosine functions?

Back

Front

How do you determine if a function is sine or cosine?

Back

You can determine this by looking at the starting point of the graph. A sine function starts at the origin (0,0), while a cosine function starts at its maximum value.

Front

What is the general form of a sine function?

Back

The general form is y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical 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 horizontal shift, and D is the vertical shift.

Front

If the amplitude of a function is 3, what does this indicate?

Back

It indicates that the maximum height of the wave from the midline is 3 units.

Front

What happens to the period of a sine or cosine function if B is increased?

Back

If B is increased, the period decreases, meaning the function completes its cycles more quickly.

Front

What is the value of the sine function at 0 degrees?

Back

The value of the sine function at 0 degrees is 0.

Front

What is the value of the cosine function at 0 degrees?

Back

The value of the cosine function at 0 degrees is 1.

Front

How do you find the period of the function y = sin(4x)?

Back