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Math Help - Finding Trig Values

  1. #1
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    Arrow [SOLVED]Finding Trig Values

    Question is:

    If A is an acute angle and CosA=4/5, find the values of,

    a) sin2A

    b) Sin3A

    c) Tan3A
    I sort of have an understanding with this question, but i dont really get it, especially part b) and part c). With a solution, can someone also leave an explanation to what they did, so i can try to understand what you did? Thanks.
    Last edited by iMan_07; December 26th 2008 at 06:03 PM.
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  2. #2
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    Quote Originally Posted by iMan_07 View Post
    Question is:



    I sort of have an understanding with this question, but i dont really get it, especially part b) and part c). With a solution, can someone also leave an explanation to what they did, so i can try to understand what you did? Thanks.
    You know from basic trigonometry, that if you consider a right angled triangle, then  cos(A) = \frac{a}{h} , where A is the angle you are considering, a is the length of the adjecent side, and h is the length of the hypotenuse.

    In this case, our triangle has adjacent side length 4, and hypotenuse of 5. Perhaps it would help if you sketched it!

    Using pythagorus, you can work out the length of the side opposite the triangle.

     o^2 = h^2 - a^2

    = 5^2-4^2

    = 25-16 = 9

     \therefore o = \sqrt{9} = 3

     o = 3

    So it's a 3,4,5 triangle! Again, from basic trigonometry, you can calculate sinA:

     sin(A) = \frac{o}{h} = \frac{3}{5} .

    So now you know sinA and cosA.

    a) You need sin2A. Remember sin2A = 2sinAcosA. You know both!

    b) You need sin3A. Remeber that sin(3A) = sin(2A+A) = sin2AcosA+cos2AsinA. And remember that  cos(2A) = (cosA)^2 - (sinA)^2 .

    c) You need tan(3A). Remember  tan(3A) = \frac{sin(3A)}{cos(3A)} . You worked out sin(3A) before, you just need cos(3A). Use the same concept of:

     cos(3A) = cos(2A+A) = cos2AcosA-sin2AsinA and   cos(2A) = (cosA)^2-(sinA)^2

    Good luck.
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  3. #3
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    Thank You soo much, wonderful explanation.
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