SOLUTION: find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. Given: cot(u)=-3, 3π/2 < u < 2π
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Question 1177237: find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. Given: cot(u)=-3, 3π/2 < u < 2π
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Since 
is in the fourth quadrant, \,<\,0)
, and \,>\,0)
.
\ =\ -3)
}{\sin(u)}\ =\ -3)
\ =\ -3\sin(u))
\ =\ 9\sin^2(u))
\ =\ 9\sin^2(u))
\ =\ 1)
\ =\ \frac{1}{10})
\ =\ \pm\frac{1}{\sqrt{10}})
But since \,<\,0\ \forall\ u\ \in \(\frac{3\pi}{2},2\pi\))
\ =\ -\frac{1}{\sqrt{10}})
Then:
\ =\ 9\ -\ 9\cos^2(u))
\ =\ 9)
\ =\ \frac{9}{10})
\ =\ \pm\frac{3}{\sqrt{10}})
But since \,>\,0\ \forall\ u\ \in \(\frac{3\pi}{2},2\pi\))
\ =\ \frac{3}{\sqrt{10}})
Next:
\ =\ 2\sin\varphi\cos\varphi)
\ =\ \cos^2\varphi\ -\ \sin^2\varphi)
\ =\ \frac{2\tan\varphi}{1\ -\ \tan^2\varphi})
Or you could just use
\ =\ \frac{\sin(2\varphi)}{\cos(2\varphi))
to get the same answer.
All you have to do is plug in the numbers and do the arithmetic.
John
My calculator said it, I believe it, that settles it
From
I > Ø
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