SOLUTION: Find sin(2x), cos(2x), and tan(2x) from the given information.
sec(x) = 4, x in Quadrant IV
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Question 1171343: Find sin(2x), cos(2x), and tan(2x) from the given information.
sec(x) = 4, x in Quadrant IV
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
QIV → cos, sec > 0; sin, csc, and tan < 0
cosine is the reciprocal of secant, so if \ = 4)
then \ =\ \frac{1}{4})
.
Then since \ =\ \pm\sqrt{1\,-\,\cos^2(\varphi)})
, but since sine is negative in QIV,
\ =\ -\sqrt{1\,-\,\frac{1}{16}}\ =\ -\frac{\sqrt{15}}{4})
Then since tangent is the quotient of sine over cosine and cosecant is the reciprocal of sine, we have:
\ =\ -\sqrt{15})
and
\ =\ -\frac{4\sqrt{15}}{15})
Then
\ =\ 2\sin(x)\cos(x))
\ =\ \cos^2(x)\ -\ \sin^2(x))
and
\ =\ \frac{2\tan(x)}{1\,-\,\tan^2(x)})
The rest is just arithmetic -- that's on you.
John
My calculator said it, I believe it, that settles it
From
I > Ø
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