Question

analyzing cofunctions
consider △abc.
what are the angles that make the trigonometric statements true?
sin(a) = cos(b)
sin(b) = cos()

Explanation:

Step1: Recall co - function identity

In a right - triangle, $\sin\theta=\cos(90^{\circ}-\theta)$. In $\triangle ABC$, if $\angle C = 90^{\circ}$, then $\angle A+\angle B = 90^{\circ}$.

Step2: Apply identity to first equation

For $\sin(A)=\cos(B)$, since $\sin\alpha=\cos(90^{\circ}-\alpha)$, when $\angle A+\angle B = 90^{\circ}$, this equation holds.

Step3: Apply identity to second equation

For $\sin(B)=\cos(x)$, and knowing $\angle A+\angle B = 90^{\circ}$, then $\sin(B)=\cos(A)$.

Answer:

$\sin(A)=\cos(B)$; $\sin(B)=\cos(A)$