Question

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

Explanation:

Step1: Recall co-function identity

For any acute angle $\theta$, $\sin(\theta) = \cos(90^\circ - \theta)$ and $\cos(\theta) = \sin(90^\circ - \theta)$. In $\triangle ABC$, $\angle C = 90^\circ$, so $\angle A + \angle B = 90^\circ$.

Step2: Solve $\sin(\square) = \cos(B)$

Since $\angle A = 90^\circ - \angle B$, substitute into identity: $\sin(A) = \cos(B)$.

Step3: Solve $\sin(B) = \cos(\square)$

Since $\angle B = 90^\circ - \angle A$, substitute into identity: $\sin(B) = \cos(A)$.

Answer:

$\sin(\boldsymbol{A}) = \cos(B)$
$\sin(B) = \cos(\boldsymbol{A})$