consider △abc. what are the angles that make the trigonometric statements true? sin( ) = cos(b) sin(b) =…
consider △abc. what are the angles that make the trigonometric statements true? sin( ) = cos(b) sin(b) = cos( )
Answer
Explanation:
Step1: Recall co - function identity
In a right - triangle, $\sin\theta=\cos(90^{\circ}-\theta)$. In right - triangle $\triangle ABC$ with right angle at $C$, $\angle A+\angle B = 90^{\circ}$.
Step2: Find the angles for the first equation
We know that $\sin(A)=\cos(B)$ because $\angle A+\angle B = 90^{\circ}$.
Step3: Find the angles for the second equation
We know that $\sin(B)=\cos(A)$ because $\angle A+\angle B = 90^{\circ}$.
Answer:
The first blank is $A$, the second blank is $A$.