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Jamierox4ev3r
 one year ago
If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and π/2, evaluate sin(x + y).
Jamierox4ev3r
 one year ago
If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and π/2, evaluate sin(x + y).

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Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 I actually have no idea what's going on here, so if you're online, I would love your help. thanks

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3recall the angle sum identity for sin : \[\sin(x+y)=\sin x\cos y + \cos x\sin y\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3basically you need to find those four pieces : \(\sin x, \cos x, ~~\sin y, \cos y\) then plug them in

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Alright, so I'm assuming that it would look a little like this: \(\sin (x + y) = (\frac{1}{3} )(\frac{5}{4})+ \sin(y)\cos(x) \)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2that's all we appear to know at this moment in time

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you 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 \(\cos y\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3so we need to find \(\cos y\), \(\sin y\) and \(\cos x\) somehow from the given info

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh whoops, completely forgot about the secant ;;

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3its easy, lets find them

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Fair enough. Let's do it

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3do you like triangles we're gonna need bunch of them

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2triangles are good with me

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441088950452:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3try finding that missing side

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2that would be \(\sqrt{8}\), I believe

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes! look at that triangle again, \(\cos x = ?\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\frac{\sqrt{8}}{3}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Awesome! just draw another triangle using \(\sec y = 5/4\) and find whatever you need

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3maybe let me draw the triangle for you

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2I think I got this

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3good, il just wait then :)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2let me try drawing it, just verify if I'm right. And thank you c:

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2dw:1441089382675:dw

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh and i forgot to draw in the right angle. but that's kind of a given

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2this actually works out really well, the missing side would simply be 3

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3yes, also the angle is \(y\), not \(x\) dw:1441089486688:dw

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh right, whoops . Since this time around we're solving for the y

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3good, find the stuff you need and see if you can finish it off!

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2dw:1441089589409:dw

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2sounds good to me :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3do let me know the final answer incase if you want me double check

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2for sure, I want to make sure I'm doing the right thing. So \(\sin y = \frac{3}{5}\) and \(\sin x = \frac{4}{5}\) then we plug all of that back in to the identity \(\large sin (x+y) = (\frac{1}{3}) (\frac{4}{5}) + (\frac{\sqrt{8}}{3}) (\frac{3}{5})\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Can this be simplified by multiplying the fractions together?

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2or would this be the final form?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3for sure, I want to make sure I'm doing the right thing. So \(\sin y = \frac{3}{5}\) and \(\color{red}{\cos y }= \frac{4}{5}\) then we plug all of that back in to the identity \(\large sin (x+y) = (\frac{1}{3}) (\frac{4}{5}) + (\frac{\sqrt{8}}{3}) (\frac{3}{5})\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2right xD I'm sort of spacing out, but that's what I have in my notebook. Totally did not type that right

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2if you looked at how I plugged things into the identity, I think it illustrates that I have a good understanding now of what's going on

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh wait, and isn't it possible for \(\sqrt{8}\) to be be simplified to \(2\sqrt{2}\)?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Ahh I see it was just a typo \(\large \sin (x+y) = (\frac{1}{3}) (\frac{4}{5}) + (\frac{\sqrt{8}}{3}) (\frac{3}{5}) = \dfrac{2(2+3\sqrt{2})}{15}\) i would leave it at that

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Yeah, that seems to be the nicest form. I got it! Thank you so much. My goodness, the calculus professor said that this was all supposed to be review. Granted, much of it is, but some of these things I feel like I've never learned before. You're a life saver, thanks a bunch!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3np btw you're doing great! I can tell, you will have no problem reviewing/learning these basic trig/functions stuff as you continue with ur calc course... just dont let these stop you from learning calc... its okay to keep coming back to these topics when you find something not so clear in ur calc course..

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Yep, that's why I'm making sure I get all the review out of the way. I'm already gaining a much better understanding, so thank you very much for your efforts. I know that all my dedication to making sure I have the basics down will pay off in the long run. An thank you also for your kind words :') It's getting pretty late for me, but I have one more question I need to ask before I leave for the day. You wouldn't mind helping me with that one as well, would you?
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