Sine and Cosine Graphs

Front

What is the cosine of an angle on the unit circle?

Back

The cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle.

Front

What is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is 2π, but can be adjusted by the coefficient of x in the function.

Front

How do you determine the amplitude of a sine or cosine graph?

Back

The amplitude is the coefficient in front of the sine or cosine function, representing the maximum distance from the midline.

Front

What is the range of the sine and cosine functions?

Back

The range of both sine and cosine functions is [-1, 1].

Front

What is the formula for the cosine function?

Back

The cosine function can be expressed as y = A cos(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

Evaluate: cos(120°)

Back

-1/2

Front

Evaluate: sin(π/4)

Back

√2/2

Front

What is the effect of changing the coefficient of x in the cosine function?

Back

Changing the coefficient of x affects the period of the graph; specifically, the period is calculated as 2π/|B|.

Front

What is the phase shift in a sine or cosine function?

Back

The phase shift is determined by the value of C in the function y = A sin(Bx + C) + D, and it shifts the graph left or right.

Front

What is the vertical shift in a sine or cosine function?

Back

The vertical shift is determined by the value of D in the function y = A sin(Bx + C) + D, moving the graph up or down.