Question

What did you notice about the maximum and minimum values of the Sine and Cosine functions? Where do they "occur"?

A. The maximum value of the Sine function is 1, and it occurs at 90 degrees. The minimum value of the Sine function is -1, and it occurs at 270 degrees. The maximum value of the Cosine function is 1, and it occurs at 0 degrees. The minimum value of the Cosine function is -1, and it occurs at 180 degrees.
B. The maximum value of the Sine function is 1, and it occurs at 180 degrees. The minimum value of the Sine function is -1, and it occurs at 0 degrees. The maximum value of the Cosine function is 1, and it occurs at 90 degrees. The minimum value of the Cosine function is -1, and it occurs at 270 degrees.
C. The maximum value of the Sine function is 1, and it occurs at 0 degrees. The minimum value of the Sine function is -1, and it occurs at 180 degrees. The maximum value of the Cosine function is 1, and it occurs at 270 degrees. The minimum value of the Cosine function is -1, and it occurs at 90 degrees.
D. The maximum value of the Sine function is 1, and it occurs at 90 degrees. The minimum value of the Sine function is -1, and it occurs at 270 degrees. The maximum value of the Cosine function is 1, and it occurs at 180 degrees. The minimum value of the Cosine function is -1, and it occurs at 0 degrees.

Answer 1

The Sine function reaches its maximum of 1 at 90 degrees and minimum of -1 at 270 degrees, while the Cosine function reaches its maximum of 1 at 0 degrees and minimum of -1 at 180 degrees.

Step-by-step explanation:

The maximum and minimum values of the Sine and Cosine functions are essential to understanding their behavior. For the Sine function, the maximum value is 1, which occurs at 90 degrees (or π/2 radians), and the minimum value is -1, occurring at 270 degrees (or 3π/2 radians). In contrast, the Cosine function has its maximum value of 1 at 0 degrees, and its minimum value of -1 at 180 degrees (or π radians).

These are the points where the Sine and Cosine graphs reach their peak amplitudes, indicating the maximum displacement in a wave or the maximum projection of a rotating vector on the y-axis (for the sine) and x-axis (for the cosine).