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# Find sin2x, cos2x,and tan2x in the given information. csc x=9, tan x <0

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Find sin2x, cos2x,and tan2x in the given information. csc x=9, tan x <0

Guest Apr 5, 2017
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### 3+0 Answers

#1
+4694
+3

csc x = 9

sin x = $$\frac{1}{9}$$

*edit* If the tangent is negative, and the sin is positive, then the cosine must be negative.

cos x = $$-\sqrt{1-(\frac{1}{9})^2}=-\frac{4\sqrt5}{9}$$

tan x = $$\frac{\sin x}{\cos x}=\frac{1}{9} \div -\frac{4\sqrt5}{9} = -\frac{\sqrt5}{20}$$

So..using the double-angle formulas:

sin (2x) = 2 sin x cos x = $$2\cdot\frac{1}{9}\cdot-\frac{4\sqrt5}{9} \mathbf{=-\frac{8\sqrt5}{81}}$$

cos (2x) = 1 - 2 sin2 x = $$1-2\cdot(\frac{1}{9})^2\mathbf{=\frac{79}{81}}$$

tan (2x) = $$\frac{2\tan x}{1-\tan^2 x}=\frac{2\cdot{ \frac{-\sqrt5}{20}}}{1- (-\frac{\sqrt5}{20})^2}=\frac{-\frac{\sqrt5}{10}}{\frac{395}{400}}\mathbf{=-\frac{8\sqrt5}{79}}$$

hectictar  Apr 5, 2017
edited by hectictar  Apr 5, 2017
#2
+4694
+2

Actually the tangent one is wrong.. I did it if tan x > 0

....Okay I think I fixed it now

hectictar  Apr 5, 2017
edited by hectictar  Apr 5, 2017
#3
+76821
+1

Yeah....you did fix it, hectictar.......check your answer for tan(2x)  by  comparing it with

sin(2x) / cos(2x)  .......

CPhill  Apr 5, 2017
edited by CPhill  Apr 5, 2017

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