anonymous
  • anonymous
Given sin (theta) = 21/29... find sin cos and tan (2 theta)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Loser66
  • Loser66
\(sin(\theta)=\dfrac{opposite}{hypotenuse}\) how about cos(theta)?
anonymous
  • anonymous
adj / hyp
Loser66
  • Loser66
ok, let them there. Now, pythagorean |dw:1435110885323:dw| Can you put numbers on the triangle?

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More answers

Loser66
  • Loser66
on that triangle, which side is hypotenuse?
anonymous
  • anonymous
left side is hyp bottom is adj and right side is opp
Loser66
  • Loser66
you use draw box below, click on it, then a box will pop up. On the right corner, you will see "copy previous drawing", click on it, then scroll up to see my picture, click it to get the pic, then put the numbers in, then post
Loser66
  • Loser66
|dw:1435111234190:dw|
Loser66
  • Loser66
hence, the adj side can be calculated by Pythagorean. Do you know him?
Loser66
  • Loser66
don't get??
anonymous
  • anonymous
oh a2 + b2 = c2
Loser66
  • Loser66
Mr. Pythagore said : In this case, \(adj = \sqrt{29^2-21^2}=??\)
Loser66
  • Loser66
knock knock!!! adj =??
Loser66
  • Loser66
Don't get or you got the answer?? If you don't answer me, I am out in 2 more minutes.
anonymous
  • anonymous
gimme one second
anonymous
  • anonymous
35.8?
Loser66
  • Loser66
redo.
anonymous
  • anonymous
wait why is it minus?
anonymous
  • anonymous
isnt the formula a squared plus b squared equals c squared?
Loser66
  • Loser66
a^2 +b^2 =c^2, hence a^2 = c^2 -b^2
anonymous
  • anonymous
ahhhh got it
anonymous
  • anonymous
so its asking for 2 theta not just theta
anonymous
  • anonymous
i got that the adj is 20
Loser66
  • Loser66
yup
Loser66
  • Loser66
now, you have all of them, plug in cos (theta) = adj/ hyp = ???
anonymous
  • anonymous
no i get that part but i need to find sin (2 theta) cos (2 thetha) and tan 2 (theta)
anonymous
  • anonymous
cos(theta) = 20/29
Loser66
  • Loser66
ok, tell me cos (theta) =??
anonymous
  • anonymous
20/29
Loser66
  • Loser66
yup
anonymous
  • anonymous
now how do i find 2 theta?
Loser66
  • Loser66
now \(sin(2\theta) = 2 sin(\theta)cos(\theta)\)
Loser66
  • Loser66
just plug numbers in, right?
anonymous
  • anonymous
ahh gotcha so cos (theta) = 2cos (0) tan (0)?
Loser66
  • Loser66
nnnnnnnnnnnnnnnnnoppppppppppe
Loser66
  • Loser66
\(cos(2\theta)= cos^2(\theta)-sin^2(\theta)\)
anonymous
  • anonymous
what is this called? i feel like i should google these formulas lol
Loser66
  • Loser66
just type double angle trig formula.
Loser66
  • Loser66
But, you should memorize some easy formulas.
anonymous
  • anonymous
got it thank you so much
Loser66
  • Loser66
ok, and you know tan = sin /cos, right?
anonymous
  • anonymous
its not 2 tan ( ) / 1 - tan ^2 ( )?
Loser66
  • Loser66
you have sin (2 theta), cos (2 theta), why don't you use them?
Loser66
  • Loser66
\(tan (\color{red}{x}) =\dfrac{sin(\color{red}{x})}{cos(\color{red}{x})}\) \(tan(\color{blue}{2x})=\dfrac{sin(\color{blue}{2x})}{cos(\color{blue}{2x})}\) got it?
anonymous
  • anonymous
oh okay makes sense
Loser66
  • Loser66
good luck. I am out now

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