Question

Which trigonometric expression has the same value as sin 38 degrees?

Answer 1

$\bf \textit{Cofunction Identities} \\ \quad \\ sin\left(\frac{\pi}{2}-{{ \theta}}\right)=cos({{ \theta}})\qquad \boxed{cos\left(\frac{\pi}{2}-{{ \theta}}\right)=sin({{ \theta}})} \\ \quad \\ \quad \\ tan\left(\frac{\pi}{2}-{{ \theta}}\right)=cot({{ \theta}})\qquad cot\left(\frac{\pi}{2}-{{ \theta}}\right)=tan({{ \theta}}) \\ \quad \\ \quad \\ sec\left(\frac{\pi}{2}-{{ \theta}}\right)=csc({{ \theta}})\qquad csc\left(\frac{\pi}{2}-{{ \theta}}\right)=sec({{ \theta}})\\\\ -------------------------------$

$\bf sin(\underline{38^o})=cos(90^o-\underline{38^o})$

Answer 2

Answer:

Option D.

Step-by-step explanation:

Trigonometric expression given in the question is sin38°.

Since we know the co-functions identity

$cos(\frac{\pi }{2}-x)=sinx$

By replacing x = 38°

$cos(\frac{\pi }{2}-38)=sin38$

cos(90°- 38°) = sin38°

Therefore, $cos(52)=sin38$

Option D. is the answer.