Question

The graphs of the sine and cosine functions cross the y-axis on the interval [−π,π]. How do the y-intercepts compare?

A. They are the same.
B. The sine function's y-intercept is greater.
C. The cosine function's y-intercept is greater.
D. It depends on the specific values of sine and cosine at π and −π.

Answer 1

The cosine function's y-intercept is greater than the sine function's y-intercept on the interval [−π,π] as the sine of 0 is 0 and cosine of 0 is 1.

Step-by-step explanation:

The question being asked is how the y-intercepts of the sine and cosine functions compare when they cross the y-axis on the interval [−π,π]. Looking at the unit circle, we know that the sine function (sin(x)) represents the y-coordinate of a point on the unit circle, whereas the cosine function (cos(x)) represents the x-coordinate of a point on the unit circle.

At x=0, which is where a function would cross the y-axis, the sine of 0 degrees (or 0 radians) is 0, and the cosine of 0 degrees (or 0 radians) is 1. This means that the sine function's y-intercept is at the origin (0,0), while the cosine function's y-intercept is at (0,1). Therefore, the correct answer to the question is: C. The cosine function's y-intercept is greater.