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Given that sinx=(1/2) in quadrant 1 and siny=(1/4) in quadrant 1, find the exact value of

sin (x+y)

i already did the question but im unsure if i did it right,

i got cosx as root 3 over 2 and cosy as root 15 over 4

if my math is correct, using the compound angle formula, i should get root 15 plus root 3 over root 8

could someone please check if i am right and if not, please explain to me how i need to get the right answer?

thank you :)

Guest May 26, 2017
#1
+89709
+2

sin ( x + y)   =   sinx cos y  +  sin y cos x

cos x  =   sqrt  ( 1 - sin^2 x)   =   sqrt [ 1 - (1/2)2 ]  = sqrt  ( 1 - 1/4)   =  sqrt (3/4)   = sqrt (3)/2

cos y  =  sqrt  ( 1 - sin^2 y )   =  sqrt [ 1 - (1/4)^2  ]  =    sqrt [ 1 - 1/16]  =   sqrt (15/16)  = sqrt (15) /4

So

sin ( x + y)   =

sinx cos y  +  sin y cos x    =

( 1/2) * sqrt(15)  /  4      +    (1/4) * sqrt (3) / 2    =

sqrt (15) / 8   +   sqrt (3) / 8  =

[ sqrt (15) + sqrt (3) ]   / 8

Correct.....!!!

CPhill  May 26, 2017
#2
+1

thank you

Guest May 26, 2017