anonymous
  • anonymous
Given: costheta= -4/5, sin x =-12/13 ,theta is in the third quadrant, and x is in the fourth quadrant; evaluate cos 2x. -119/169 119/169 -11/13
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
you don't need the sine part
anonymous
  • anonymous
then how do I start
terenzreignz
  • terenzreignz
Two variables?

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anonymous
  • anonymous
\[\cos(2x)=2\cos^2(x)-1\]
anonymous
  • anonymous
|dw:1364529999084:dw|
anonymous
  • anonymous
oh i see there is a \(\theta\) and an \(x\)
anonymous
  • anonymous
costheta= -4/5 I need cosx
anonymous
  • anonymous
you are asked for \(\cos(2x)\) where \(\sin(x)=-\frac{12}{13}\)
anonymous
  • anonymous
\[\cos(2x)=1-2\sin^2(x)\]
anonymous
  • anonymous
When I do it I get 169
anonymous
  • anonymous
a denominator of 169
anonymous
  • anonymous
there is no \(\theta \) in your question
anonymous
  • anonymous
ok, I'll do it for you, give me a second, this is an easy question
anonymous
  • anonymous
yea I had to put theta for that
anonymous
  • anonymous
satellite, you don't know what you're doing..
anonymous
  • anonymous
\[\cos(x)=1-2\sin^2(x)\] \[\cos(x)=1-(\frac{-12}{13})^2\]\
anonymous
  • anonymous
there is your 169
anonymous
  • anonymous
\[\cos(2x)=1-(\frac{12}{13})^2\] \[\cos(2x)=1-\frac{144}{169}\]
anonymous
  • anonymous
\[\cos(2x)=\frac{25}{169}\]
anonymous
  • anonymous
I know, thats what I get, but it isnt a choice
anonymous
  • anonymous
your question asks for \(\cos(2x)\) and doesn't mention any \(\theta\)
anonymous
  • anonymous
I know but that is what is already given
anonymous
  • anonymous
oh damn i made a mistake!! sorry
anonymous
  • anonymous
I'm too lazy to do it but you need to draw the triangles and either use theta or x for the angle
anonymous
  • anonymous
lol its okay, Ive made plenty
anonymous
  • anonymous
\[\cos(2x)=1-2\sin^2(x)\] \[\cos(2x)=1-2\times (\frac{12}{13})^2\] \[cos(2x)=1-2\times \frac{144}{169}\]
anonymous
  • anonymous
\[\cos(2x)=1-\frac{288}{169}\]\[\cos(2x)=-\frac{119}{169}\]
anonymous
  • anonymous
Lol this is a lot of work, can you use this same formula for tan2Theta
anonymous
  • anonymous
nvm. I found the formula, Thank you!

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