before-calculus

Question

sinu=12/37 sinv=35/37, u and v are between 0, pi/2 find cos(u+v) exactly

Answer 1

Observe that 12, 35, 37 form a Pythagorean Triple: 12² + 35² = 37² and form a right triangle.

If sin U = 12 / 37, and U is in the first quadrant, then cos U = 35 / 37.

Also, if sin V = 35 / 37, then U and V have to be complimentary: U + V = 90.

Thus, cos (U + V) = cos( 90 ) = 0.