SOLUTION: Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 4, tan x < 0
sin 2x =
cos 2x =
tan 2x =
Algebra.Com
Question 667427: Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 4, tan x < 0
sin 2x =
cos 2x =
tan 2x =
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{1}{\sin\left(\varphi\right)})
Hence, \ =\ \frac{1}{4})
But since ^2\ +\sin\left(\varphi\right)^2\ =\ 1)
, \ =\ \pm\frac{\sqrt{15}}{4})
.
But since the tangent is the sine divided by the cosine and we have a positive sine value, and are given that the tangent is negative, the cosine must be negative. Hence:
\ =\ -\frac{\sqrt{15}}{4})
Using the double angle formulae:
\ =\ 2\sin\left(\varphi\right)\cos\left(\varphi\right))
\ =\ 2\left(\frac{1}{4}\right)\left(-\frac{\sqrt{15}}{4}\right)\ =\ -\frac{\sqrt{15}}{8})
\ =\ \cos^2\left(\varphi\right)\ -\ \sin^2\left(\varphi\right))
\ =\ \frac{15}{16}\ -\ \frac{1}{16}\ =\ \frac{7}{8})
Then since:
\ =\ \frac{\sin\left(\varphi\right)}{\cos\left(\varphi\right)})
\ =\ \frac{\sin\left(2x\right)}{\cos\left(2x\right)}\ =\ \frac{\frac{-\sqrt{15}}{8}}{\frac{7}{8}}\ =\ -\frac{\sqrt{15}}{7})
John
My calculator said it, I believe it, that settles it
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