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Math Help - Help with Double Angle Identities!!!

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    Help with Double Angle Identities!!!

    cos θ = 24/25

    The angle lies in quadrant 1; 0<θ<90

    Find sin2θ



    I know you would use either the formula cos^2θ - sin^2θ or 2sinθcosθ
    And I know that the answer is 339/625, but I do not know how to get that answer?
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    Re: Help with Double Angle Identities!!!

    Quote Originally Posted by whittwhitt View Post
    cos θ = 24/25

    The angle lies in quadrant 1; 0<θ<90

    Find sin2θ



    I know you would use either the formula cos^2θ - sin^2θ or 2sinθcosθ
    And I know that the answer is 339/625, but I do not know how to get that answer?
    Well, you know sin(theta) since you know cos(theta). And sin(2theta) = 2 sin(theta) cos(theta)....

    -Dan
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    Re: Help with Double Angle Identities!!!

    Yes, you use one of those but which? One is sin(2\theta) and which is cos(2\theta)? (What happens if \theta= 0?)

    If cos(\theta)= 24/25 and \theta is in the first quadrant what is sin(\theta)? (You do know that sin^2(\theta)+ cos^2(\theta)= 1, don't you?
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    Re: Help with Double Angle Identities!!!

    Let me see ... is your difficulty that you work the problem out, but you get an answer different from 339/625?

    If so, maybe you answer is right. I also get something different from 339/625.

    Could you show us what you did to find your answer.?
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    Re: Help with Double Angle Identities!!!

    My teacher gave us the answers so that we could check to see if we were doing the problem right.
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    Re: Help with Double Angle Identities!!!

    Well, he might've made a typo or something. What answer do you get?
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    Re: Help with Double Angle Identities!!!

    Could you guys help me with one more problem? ... I promise I wrote this one down correctly

    Thank you!

    Could you help me with another problem?

    secθ = -(sqrt41)/4
    In quadrant 3; cosθ > 0
    Find sin2θ
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  8. #8
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    Re: Help with Double Angle Identities!!!

    This is the same kind of problem as the last one. Only you say cos(theta) > 0? In quadrant III, cos < 0, or so I believe. Am I wrong? Do you mean that cos(2 theta) > 0?

    Oh, I see. You mean that sin(theta) < 0. In quadrant 3 both functions > 0. That means theta > pi, so 2*theta > 2pi, the answer is probably in quadrant 1. You'd expect the sin(2 theta) to be > 0, right?
    Last edited by zhandele; November 27th 2012 at 05:20 PM. Reason: afterthought
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    Re: Help with Double Angle Identities!!!

    I have to go to sleep now, but do you know the first step to take? I'll give you a hint if not.
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