Question

practice 5 (from unit 4, lesson 8)
consider this equation: \\(sin(30^{\circ}) = cos(\theta)\\). what value of \\(\theta\\) makes this equation true?
a \\(-30\\)
b \\(30\\)
c \\(60\\)
d \\(180\\)

Explanation:

Step1: Recall co-function identity

We know the co - function identity in trigonometry: $\sin(\alpha)=\cos(90^{\circ}-\alpha)$.

Step2: Apply the identity to the given equation

Given the equation $\sin(30^{\circ})=\cos(\theta)$. Using the co - function identity $\sin(\alpha)=\cos(90^{\circ}-\alpha)$, when $\alpha = 30^{\circ}$, we have $\sin(30^{\circ})=\cos(90^{\circ}-30^{\circ})=\cos(60^{\circ})$. So $\theta = 60^{\circ}$.

Answer:

C. 60