Question

use the diagram to complete the statement. given △jkl, sin(38°) equals ○ cos(38°) ○ cos(52°) ○ tan(38°) ○ tan(52°)

Explanation:

Step1: Recall co - function identity

In a right - triangle, we know the co - function identity: \(\sin\theta=\cos(90^{\circ}-\theta)\).
In right - triangle \(JKL\) with right angle at \(J\), we know that the sum of the angles in a triangle is \(180^{\circ}\), and since \(\angle J = 90^{\circ}\), \(\angle K=52^{\circ}\) and \(\angle L = 38^{\circ}\), we can use the co - function identity.
We want to find what \(\sin(38^{\circ})\) is equal to. Let \(\theta = 38^{\circ}\), then \(90^{\circ}-\theta=90 - 38=52^{\circ}\).
According to the co - function identity \(\sin\theta=\cos(90 - \theta)\), when \(\theta = 38^{\circ}\), \(\sin(38^{\circ})=\cos(90 - 38)^{\circ}=\cos(52^{\circ})\).

Answer:

\(\cos(52^{\circ})\) (the option corresponding to \(\cos(52^{\circ})\))