Respuesta :
[tex]\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}})\\\\
-------------------------------[/tex]
[tex]\bf sin(\underline{38^o})=cos(90^o-\underline{38^o})[/tex]
[tex]\bf sin(\underline{38^o})=cos(90^o-\underline{38^o})[/tex]
Answer:
Option D.
Step-by-step explanation:
Trigonometric expression given in the question is sin38°.
Since we know the co-functions identity
[tex]cos(\frac{\pi }{2}-x)=sinx[/tex]
By replacing x = 38°
[tex]cos(\frac{\pi }{2}-38)=sin38[/tex]
cos(90°- 38°) = sin38°
Therefore, [tex]cos(52)=sin38[/tex]
Option D. is the answer.
