How are the sin 70° and the cos 20° related? Explain using complete sentences.

Question

 show all work using numbers and letters

Answer 1

The "cosine" is short for "complementary sine", or the sine of the complementary angle in a right triangle.  70^o and 20^o are complementary angles, meaning they add up to 90^o.  So the cosine of 20^o is the same as the sine of its complementary angle, 70^o; that is cos(20^o) = sin(70^o).  The identity that captures this is cos(90^o - x) = sin(x), where 90^o - x is the complement of x.

 

So if x = 70^o:

 

cos(90^o-70^o) = sin(70^o)

cos(20^o) = sin(70^o)