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

Question

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

Answer 1

sin45= cos45 or sin(pi/4) = cos(pi/4) = sqr2/2 = about 0.707

45 degrees is an acute angle

sin(a) = cos(90-a)

90-a = a

2a =90

a = 90/2 = 45

sin225 = cos225 or sin(5pi/4) = cos(5pi/4) but 225 is not an acute angle,