# Compound Angle Question

• August 31st 2012, 12:14 PM
waleedrabbani
Compound Angle Question
Determine Sin(x+y)

If Sinx = 4/5 Cosy = 12/13

Therefore the following is true.
sinx = 4/5
cosx = (+/-)3/5
siny = (+/-)5/12
cosy = 12/13
Angle X can be in Quadrant 1 or 2
Angle Y can be in Quadrant 1 or 4

s(x+y) = (4/5)(12/3) + (3/5)(5/12)
= 63/65

My Question is, that is this the only solution or do i have to plug in the negative values of cosx and siny in the equation to get different answers?

Thanks Alot
• August 31st 2012, 03:20 PM
skeeter
Re: Compound Angle Question
Quote:

i have to plug in the negative values of cosx and siny in the equation to get different answers
you do if the quadrants for angles x and y were not specified ...
• August 31st 2012, 04:18 PM
MaxJasper
Re: Compound Angle Question
$x=\left\{\sin ^{-1}\left(\frac{4}{5}\right),\pi -\sin ^{-1}\left(\frac{4}{5}\right)\right\}$

$y=\left\{\cos ^{-1}\left(\frac{12}{13}\right),2 \pi -\cos ^{-1}\left(\frac{12}{13}\right)\right\}$