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find sin 2x

if tan x=2 cosx>0

  • trig -

    first 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 -

    since 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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