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, for complementary angles $\alpha$ and $\beta$ ($\alpha+\beta = 90^{\circ}$), $\sin\alpha=\cos\beta$.

Step2: Identify complementary angles

In right - triangle $\triangle{JKL}$, $\angle{L}=38^{\circ}$ and $\angle{K}=52^{\circ}$, and $38^{\circ}+52^{\circ}=90^{\circ}$.

Step3: Apply co - function identity

We know that $\sin(38^{\circ})=\cos(90^{\circ}-38^{\circ})=\cos(52^{\circ})$.

Answer:

$\cos(52^{\circ})$