Question

(c) choose the correct statement.
for any angle θ, we have sin(−θ)=sinθ. (so sine is an even function.)
for any angle θ, we have sin(−θ)=−sinθ. (so sine is an odd function.)
neither of the above answers are true. (so sine is neither an odd nor an even function.)

Explanation:

Step1: Recall the definitions of odd and even functions

An even function satisfies $f(-x)=f(x)$ and an odd - function satisfies $f(-x)=-f(x)$. For the sine function $y = \sin(x)$, we check $\sin(-\theta)$.

Step2: Use the unit - circle or trigonometric identities

By the unit - circle definition or trigonometric identities, for any angle $\theta$, $\sin(-\theta)=-\sin(\theta)$. This means the sine function is an odd function.

Answer:

For any angle $\theta$, we have $\sin(-\theta)=-\sin\theta$. (So sine is an odd function.)