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Math Help - [URGENT!!] Trig - Compound Angles Formulas and Cofunction Identities

  1. #1
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    [URGENT!!] Trig - Compound Angles Formulas and Cofunction Identities

    Question:
    Given 2pi/3 = pi/2 + pi/6. Find sin(2pi/3)



    My Work:

    cos(pi/2 + pi/6)
    = (cos pi/2)(cos pi/6) - (sin pi/2) (sin pi/6)
    = (square root of 3 / 2) (square root of 3 / 2) - (2/2) (1/2)
    = square root of 9/ 4 - 2/4
    = 3-2/4
    = 1/4

    When I found the values (in decimal) for both the question (-0.5) and my answer (0.25), they are not equal to one another and they're suppose to be ...
    What am I doing wrong?

    P.S. - you need to use the special triangles to find the exact values from the radians
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  2. #2
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    Quote Originally Posted by Macleef View Post
    Question:
    Given 2pi/3 = pi/2 + pi/6. Find sin(2pi/3)



    My Work:

    cos(pi/2 + pi/6)
    = (cos pi/2)(cos pi/6) - (sin pi/2) (sin pi/6)
    = (square root of 3 / 2) (square root of 3 / 2) - (2/2) (1/2)
    = square root of 9/ 4 - 2/4
    = 3-2/4
    = 1/4

    When I found the values (in decimal) for both the question (-0.5) and my answer (0.25), they are not equal to one another and they're suppose to be ...
    What am I doing wrong?

    P.S. - you need to use the special triangles to find the exact values from the radians
    You have the concept correctly, but there are actually two things you did wrong:

    cos(pi/2 + pi/6)
    = (cos pi/2)(cos pi/6) - (sin pi/2) (sin pi/6)
    = (square root of 3 / 2) (square root of 3 / 2) - (2/2) (1/2)
    = square root of 9/ 4 - 2/4
    = 3-2/4
    = 1/4

    Going from cos pi/2, you got sqrt of 3/2 which is wrong. I don't know how you did that. pi/2 is not a special triangle angle, so you can't figure out using them. However, since its pi/2, meaning 180 degrees over 2, meaning 90 degrees, we know that it is on the 90 degree axis when we draw the cartesian plane. Assuming that the radius is 1 (because it is for all unit circles), then we know that the point is (0,1). 0 is the x-coordinate because it lies on the axis, and 1 is the y coordinate. I don't know if you've learned this before or not, if you haven't it probably seems confusing. Also, this is a quick way to remember this method "SYRCXRTYX" Sine is y/r cos is x/r and tan is y/x. Since its COS pi/2, we go to the 90 degree coordinate, and since its cos, we use x/r. x being 0 and r 1. Therefore, your answer is cos 0/1 which is 0.

    The Sine of pi/2 is the same concept, except we use SYR; sine is y/r. y is 1, and r is 1, meaning it is 1. That gives you:


    cos(pi/2 + pi/6)
    = (cos pi/2)(cos pi/6) - (sin pi/2) (sin pi/6)
    = (0) (square root of 3 / 2) - (1) (1/2)
    = - (1)(1/2)
    = -0.5

    And that's the correct answer. Hope that helped. Just remember that you cannot use the speciale triangles for pi/2, since it isnt an angle there.
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