Let α and β be two acute angles of a right triangle in a unit circle. (Thus α and β are complementary angles.)

Question

a. Show that sin⁡(α)=cos⁡(β) and sin⁡(β)=cos⁡(α)

b.

 Under what conditions will sin⁡(α)=cos⁡(α)

Answer 1

sinA = cos(90-A)

sin60 = cos30

sin30 = cos60

sin22 = cos68

sin87 = cos3

sin45 = cos45

sin(pi/4) = cos(pi/4)

sin(5pi/4) = cos(5pi/4)

sin(225) = cos(225)