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September 23, 2014

September 23, 2014

Posted by **Hayden** on Wednesday, February 18, 2009 at 4:54pm.

if tan x=2 cosx>0

- trig -
**Damon**, Wednesday, February 18, 2009 at 5:17pmfirst quadrant because sin and cos are +

triangle is 1, 2, sqrt 45

sin x = 2/sqrt 5

cos x = 1/sqrt 5

I think you can take it from there

- trig -
**Reiny**, Wednesday, February 18, 2009 at 5:22pmsince both the cosine and the tangent are positive, x must be an angle in the first quadrant.

from tanx = 2/1, draw a right-angled triangle with angle x at the origin that has a height of 2, and a base of 1

(tangentx = opposite/adjacent, so the opposite is 2 and the adjacent is 1)

so by Pythagoras, the hypotenuse is √5

so sinx - 2/√5 and cosx = 1/√5

sin2x = 2sinxcosx (one of our general identities)

= 2(2/√5)(1/√5) = 4/5

you can check this on the calculator

take inverse tan of 2 to get the angle,

double that angle

take the sine

you should get .8 which is 4/5

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