If the two acute angles of a right triangle are labeled A and B, what is the relationship between sin A and cos B and between sin B and cos A?

Question

Use a 30°-60°-90° triangle to justify the conjecture

Answer 1

A and B are complementary, they add up to 90 degrees.

so A + B = 90

 

this means A = 90 - B  and B = 90 - A

 

 sin A = cos (90 - A) = cos (B)

 

 sin B = cos ( 90 - b) = cos(A) 

 

cos A = sin (90-A) = sin B

 

cos B = sin (90 - B) = sin A