+322 I have no idea how to do this. I tried approaching it in different ways but got it wrong each time.
Find the exact value of the trigonometric expression given that sin u = (7/25) and cos v = (−8/17).
(Both u and v are in Quadrant II.) (Has to be a fraction, integer, or exact decimal)
sin(u + v)
+129852 sin ( u + v) = sin u cos v + sin v cos u
Note...sin v = sqrt [ 1 - cos^2v] = sqrt [ 1 - (-8/17)^2] = sqrt [ 1 - 64 / 289] = sqrt [ [289 - 64 ] / 289] = sqrt[ 225/289] = 15/17...and this is positve in Q2
cos u = sqrt [ 1 - sin ^2u ] = sqrt [ 1 - (7/25)^2 ] = sqrt [ 1 - 49 / 625 ] = sqrt [ [625- 49]/ 625 ]=
sqrt [ 576/ 625] = 24 / 25....but...this is Q2 angle so cos u = -24/25
So...we have
7/25 * -8 /17 + 15 /17 * -24 / 25 =
[-56 - 360] / [ 425 =
-416 / 425
