ILL FAN AND GIVE A MEDAL TO WHOEVER CAN GIVE ME THE CORRECT ANSWER AND HELP WITH THIS!:)

Find the exact value for sin(x + y) if sin(x) = -4/5 and cos(y) = 15/17. Angles x and y are in the fourth quadrant.

Thanks in advance to whoever does!

Question

ILL FAN AND GIVE A MEDAL TO WHOEVER CAN GIVE ME THE CORRECT ANSWER AND HELP WITH THIS!:)

Find the exact value for sin(x + y) if sin(x) = -4/5 and cos(y) = 15/17. Angles x and y are in the fourth quadrant.

Thanks in advance to whoever does!

kc_kennylau · Answer

remember $\sin^2x+\cos^2x=1$ :D
(corollary: $\sin x=\sqrt{1-\cos^2x}$ and $\cos x=\sqrt{1-\sin^2x}$

and you can use the formula $\sin(x+y)=\sin x\cos y+\cos x\sin y$

kc_kennylau · Answer

hope that helps you :D

anonymous · Answer

omgosh, i dont know what any of that means :c lol I'm great in pretty much every other subject, but trigonometry will be the death of me. haha Thanks for trying though !

kc_kennylau · Answer

just use the formula $\sin(x+y)=\sin x\cos y+\cos x\sin y$ :)

kc_kennylau · Answer

and substitute the values into that formula

anonymous · Answer

so sin(-4/5+15/7)=my answer??

kc_kennylau · Answer

no :/

kc_kennylau · Answer

$\sin(x+y)=\sin x\cos y+\cos x\sin y=-\frac45*\frac{15}{17}+\cos x\sin y$

anonymous · Answer

that's the equation? how in the world did you get that??

kc_kennylau · Answer

that's an identity: $\sin(x+y)=\sin x\cos y+\cos x\sin y$

kc_kennylau · Answer

you just have to use this identity

kc_kennylau · Answer

you are finding $\sin(x+y)$, which is equivalent to $\sin x\cos y+\cos x\sin y$, so you substitute the numbers in there to find its value

anonymous · Answer

soooo, -4/5*15/7+15/5*-4/7?? :)

kc_kennylau · Answer

no...

kc_kennylau · Answer

ok draw two right triangles, one for x and one for y

kc_kennylau · Answer

you'll have to use PythThm

anonymous · Answer

|dw:1384923382558:dw|

kc_kennylau · Answer

|dw:1384923464460:dw|

kc_kennylau · Answer

find the other two sides

anonymous · Answer

okay, 3 and 16? but how is a side of a triangle negative?

kc_kennylau · Answer

because it's in the fourth quadrant and everything in the fourth quadrant is cool
(8^2+15^2=17^2)

anonymous · Answer

lol so its negative because its cool? that makes sense :P lmao buttt was i right baout the 3 and 16? and what is that equation u put there??

kc_kennylau · Answer

it's not 16 it's 8 (8^2+15^2=17^2)

kc_kennylau · Answer

and can i finish my lunch first i'm so sorry

anonymous · Answer

lol yeah im in no rush, thanks for all of this. lol and lunch? its 11 o clock at night hereee ahaa

kc_kennylau · Answer

hi im back :)

anonymous · Answer

hey sorry i wasnt at my computer, but i finally found the answer to that one on google. because no matter how long i looked at all of the above and tried to figure it out, I COULDNT DO IT,, so i gave up and cheated :l

kc_kennylau · Answer

@kittiwitti1 maybe you can help him :D