Question

if the sin 90° = 1, then which statement is true? cos 0° = 1, because the angles are complements cos 90° = 1, because the angles are supplements cos 0° = 0, because the angles are complements cos 90° = 0 because the angles are supplements

Explanation:

Step1: Recall co - function identity

The co - function identity states that $\sin\theta=\cos(90^{\circ}-\theta)$ for complementary angles. The angles $90^{\circ}$ and $0^{\circ}$ are complementary since $90^{\circ}+ 0^{\circ}=90^{\circ}$.

Step2: Evaluate cosine of complementary angle

We know that $\sin90^{\circ} = 1$. By the co - function identity $\sin\alpha=\cos(90^{\circ}-\alpha)$. When $\alpha = 90^{\circ}$, then $\cos(90^{\circ}-90^{\circ})=\cos0^{\circ}$. And we know that $\cos0^{\circ}=1$.

Answer:

$\cos0^{\circ}=1$, because the angles are complements