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Thread: Trigonometry Questions

  1. #1
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    Trigonometry Questions

    Hello, I've got a few questions that I need help with. I'm not sure how to do these, and any help is appreciated!

    1) Solve algebraically the equation √3tan2x = 1, for 0 <= x <= Pi.
    2) By expanding cos(x+y) show that the exact value of cos(x+y) is 3/5, where sinx = 7/25, and cosx = 20/25.
    3) Solve the equation sinx°cos20° - cosx°sin20° = 4/9 for 0 < x < 180.

    Thanks in advance!
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  2. #2
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    Re: Trigonometry Questions

    Quote Originally Posted by Influence View Post
    Hello, I've got a few questions that I need help with. I'm not sure how to do these, and any help is appreciated!

    1) Solve algebraically the equation √3tan2x = 1, for 0 <= x <= Pi.
    Tan2x is like y at the start. If √3 y =1, then y =1/√3.
    So tan2x =1/√3. Now tan of what angle equals 1/√3. Let 2x equal that number. Then divide by 2.
    Thanks from Influence
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    Re: Trigonometry Questions

    Quote Originally Posted by JaguarXJS View Post
    Tan2x is like y at the start. If √3 y =1, then y =1/√3.
    So tan2x =1/√3. Now tan of what angle equals 1/√3. Let 2x equal that number. Then divide by 2.
    Ah, that makes sense! I just tried that, and got the answer that it was wanting! Thanks a lot! Have you got any idea how to do the other two??
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    Re: Trigonometry Questions

    Quote Originally Posted by Influence View Post
    2) By expanding cos(x+y) show that the exact value of cos(x+y) is 3/5, where sinx = 7/25, and cosx = 20/25.
    First I assume you have a typo and that cosy = 20/25. cos(x+y) = cosxcosy-sinxsiny. You have the exact values of sinx and cosy. Now draw 2 right triangles, one using an angle x and another using angle y. Find the length of all sides. 4 sides are basically given to you. How do you thing you find the other 2 sides?
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    Re: Trigonometry Questions

    Quote Originally Posted by JaguarXJS View Post
    First I assume you have a typo and that cosy = 20/25. cos(x+y) = cosxcosy-sinxsiny. You have the exact values of sinx and cosy. Now draw 2 right triangles, one using an angle x and another using angle y. Find the length of all sides. 4 sides are basically given to you. How do you thing you find the other 2 sides?
    Yeah, sorry, that's a typo. I've used Pythagoras theorem to find the missing sides. On the sinx triangle, the missing side has a length of 24, and on the cosy triangle the missing side is 15? So, I'm guessing all I do now is use these values, along with the cosxcosy-sinxsiny equation, and use that to get my answer??
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