Find the exact value of the trigonometric function given that sin u = − 3 5 and cos v = − 9 41 . (Both u and v are in Quadrant III.) sin(u + v)

Answer 1

Hi Tolani A.,

With sin(θ) = y/h, and cos(θ) = x/h (h-hypotenuse), and h² = x² + y²:

For sin(u) = -3/5 in the third quadrant (x and y are negative) gives: y = -3, h = 5, and x = -4. (3-4-5 triangle).

For cos(v) = -9/41 in the third quadrant gives: x = -9, h = 41, and y = -40 (y = -√[41² - (-9)²]).

So cos(u) = x/h = -4/5, and sin(v) = y/h = -40/41

sin(u + v) = sin(u)*cos(v) + cos(u)*sin(v)

sin(u + v) = (-3/5)*(-9/41) + (-4/5)*(-40/41) = 187/205

I hope this helps, Joe.