Question

If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and π/2, evaluate sin(x + y).

Answer 1

@ganeshie8 I actually have no idea what's going on here, so if you're online, I would love your help. thanks

Answer 2

recall the angle sum identity for sin :
\[\sin(x+y)=\sin x\cos y + \cos x\sin y\]

Answer 3

basically you need to find those four pieces : \(\sin x, \cos x, ~~\sin y, \cos y\)
then plug them in

Answer 4

Alright, so I'm assuming that it would look a little like this:

\(\sin (x + y) = (\frac{1}{3} )(\frac{5}{4})+ \sin(y)\cos(x) \)

Answer 5

that's all we appear to know at this moment in time

Answer 6

you have the correct idea
but we don't really know the value of \(\cos y\) yet, what we're given is \(\sec y\) and not \(\cos y\)

Answer 7

so we need to find \(\cos y\), \(\sin y\) and \(\cos x\) somehow from the given info

Answer 8

oh whoops, completely forgot about the secant ;-;

Answer 9

riiight

Answer 10

its easy, lets find them

Answer 11

Fair enough. Let's do it

Answer 12

do you like triangles
we're gonna need bunch of them

Answer 13

triangles are good with me