Question

which of the following is not a characteristic of the cosine function?
choose the correct answer.
a. the cosine function obtains a relative maximum at $x = 2\pi n$ where n is an integer.
b. the cosine function is an even function, which means that $\cos(-x)=\cos x$.
c. the x-intercepts or zeros of the cosine function are of the form $x = \frac{(2n + 1)}{2}\pi$ where n is an integer.
d. the y-intercept is 0.

Explanation:

• For option A: The cosine function $y=\cos x$ has a maximum value of 1, achieved when $x=2n\pi$ (n is integer), so this is a valid characteristic.
• For option B: An even function satisfies $f(-x)=f(x)$, and $\cos(-x)=\cos x$, so this is a valid characteristic.
• For option C: The zeros of $y=\cos x$ occur when $\cos x=0$, which solves to $x=\frac{(2n+1)\pi}{2}$ (n is integer), so this is a valid characteristic.
• For option D: The y-intercept is found by setting $x=0$, so $\cos(0)=1$, not 0. This is not a characteristic of the cosine function.

Answer:

D. The y-intercept is 0.