Graphing Sine and Cosine

Front

What is the sine function?

Back

The sine function, denoted as sin(x), is a trigonometric function that relates the angle x (in radians) to the ratio of the length of the opposite side to the hypotenuse in a right triangle.

Front

What is the cosine function?

Back

The cosine function, denoted as cos(x), is a trigonometric function that relates the angle x (in radians) to the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1.

Front

What is the range of the cosine function?

Back

The range of the cosine function is from -1 to 1.

Front

What is the period of the sine function?

Back

The period of the sine function is 2π.

Front

What is the period of the cosine function?

Back

The period of the cosine function is 2π.

Front

How do you graph the sine function?

Back

To graph the sine function, plot points for key angles (0, π/2, π, 3π/2, 2π) and connect them in a smooth wave pattern.

Front

How do you graph the cosine function?

Back

To graph the cosine function, plot points for key angles (0, π/2, π, 3π/2, 2π) starting at (0,1) and connect them in a smooth wave pattern.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the wave, calculated as |A| in the function y = A sin(Bx) or y = A cos(Bx).

Front

What does a phase shift in a sine or cosine function represent?

Back

A phase shift represents a horizontal shift of the graph, determined by the value of C in the function y = A sin(B(x - C)) or y = A cos(B(x - C)).