Question

Which angle is an x-intercept for the function y = cos(1) A.0 B.2 C. £ D. 2£

Answer 1

Answer: C. $\pi$

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Explanation:

The x intercept always occurs when y = 0.

Use the unit circle to determine that $\cos(\theta) = 0$ when $\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}$

So if $x = \pi$, then we have

$y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0$

which shows us that $(\pi, 0)$ is the location of one of the infinitely many x intercepts for this function.