Question

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

Explanation:

The definition of an odd - function is \(f(-x)=-f(x)\) and for an even - function is \(f(-x) = f(x)\). For the sine function \(y = \sin(x)\), \(\sin(-\theta)=-\sin(\theta)\) for any angle \(\theta\), which satisfies the definition of an odd - function.

Answer:

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