Given sin (theta) = 21/29... find sin cos and tan (2 theta)

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Given sin (theta) = 21/29... find sin cos and tan (2 theta)

Mathematics
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\(sin(\theta)=\dfrac{opposite}{hypotenuse}\) how about cos(theta)?
adj / hyp
ok, let them there. Now, pythagorean |dw:1435110885323:dw| Can you put numbers on the triangle?

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

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