Question

question 1 (multiple choice worth 4 points)
(05.02 mc)
if the sin 0° = 0, then which statement is true?
o cos 90° = 1, because the angles are complements
o cos 180° = 1, because the angles are supplements
o cos 90° = 0, because the angles are complements
o cos 180° = 0, because the angles are supplements

Explanation:

Step1: Recall trigonometric values

We know that $\cos90^{\circ}=0$ (not $1$), so the option “$\cos90^{\circ}=1$, because the angles are complements” is wrong. Also, $\cos180^{\circ}=- 1$ (not $0$ or $1$), so the options “$\cos180^{\circ}=0$, because the angles are supplements” and “$\cos180^{\circ}=1$, because the angles are supplements” are wrong.

Step2: Check the relationship of complementary angles

Complementary angles add up to $90^{\circ}$. The co - function identity states that $\sin\theta=\cos(90^{\circ}-\theta)$. When $\theta = 0^{\circ}$, $\sin0^{\circ}=\cos90^{\circ}$. Since $\sin0^{\circ}=0$, then $\cos90^{\circ}=0$ as they are related by the complementary angle relationship.

Answer:

$\cos90^{\circ}=0$, because the angles are complements.