Question

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

A- tan 38
B cos 38
C tan 52
D cos 52

Answer 1

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


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

Answer 2

Option D.

Explanation:

Trigonometric expression given in the question is sin38°.

Since we know the co-functions identity

`cos((\pi )/(2)-x)=sinx`

By replacing x = 38°

`cos((\pi )/(2)-38)=sin38`

cos(90°- 38°) = sin38°

Therefore,
`cos(52)=sin38`

Option D. is the answer.