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Math Help - Finding angle/ Double angle formula

  1. #1
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    Finding angle/ Double angle formula

    I am studying for a test and cannot figure out how to do these two questions.

    1. Find the angle,θ, between the positive x-axis and a line segment joining the origin and a variable point (x, x+1) on the graph of y=x+1

    2. Using the double angle formula sin2θ=2sinθcosθ find all θ, 0<θ<2pi,
    such that sin2θ=sinθ

    Thanks!
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  2. #2
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    For the first one draw the diagram.
    Then create the right triangle of base x and height x^2+1.
    Now, \tan{\theta}=\frac{x^2+1}{x}.
    That's pretty much all there is to it.



    Number 2 is just simple substitution.

    \sin{2\theta}=\sin{\theta}
    2\sin{\theta}\cos{\theta}=\sin{\theta}
    2\cos{\theta}=1
    \cos{\theta}=\frac{1}{2}
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Isosceles Kramer View Post
    For the first one draw the diagram.
    Then create the right triangle of base x and height x^2+1.
    Now, \tan{\theta}=\frac{x^2+1}{x}.
    That's pretty much all there is to it.



    Number 2 is just simple substitution.

    \sin{2\theta}=\sin{\theta}
    2\sin{\theta}\cos{\theta}=\sin{\theta}
    2\cos{\theta}=1
    \cos{\theta}=\frac{1}{2}
    Number 2 should be solved via factoring in order to get all the solutions:

    2sin{\theta}cos{\theta} - sin{\theta} = 0

    sin{\theta}(2cos{\theta}-1) = 0

    sin{\theta} = 0 \text { or } cos{\theta} = \frac{1}{2}
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