Advanced Functions Trigonemetry
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 :)
+128407
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.....!!!
