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# Sum and Difference Formulas

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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)

Nov 7, 2018

### 2+0 Answers

#1
+1 Nov 7, 2018
#2
+1

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   Nov 7, 2018