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-   -   Need to complete this identity (https://www.askmehelpdesk.com/showthread.php?t=346430)

  • Apr 26, 2009, 06:31 PM
    sdlinsey
    need to complete this identity
    1 - 1/2 sin(2theta) = ?
  • Apr 26, 2009, 07:40 PM
    Unknown008



    1. treat as a single term and solve for it normally. You'll end up with:



    2. However, this equation had no solutions since the sine curve never cuts the line y = 2. This ends your question.

    Or, if that was:

    1. Same procedure but end up with



    2. Find the key angle (here denoted by alpha);





    3. Determine the quadrants in which the angle is found, here it is in the first and second quadrant, where sine is both positive.

    4. Equate to your obtained angles, you'll have



    5. Finally solve for theta, you'll have 15 and 75 in degrees.
  • Apr 26, 2009, 07:50 PM
    sdlinsey
    No see the answer has to be in sin and cos


    Quote:

    Originally Posted by Unknown008 View Post


    1. treat as a single term and solve for it normally. You'll end up with:



    2. However, this equation had no solutions since the sine curve never cuts the line y = 2. This ends your question.

    Or, if that was:

    1. Same procedure but end up with



    2. Find the key angle (here denoted by alpha);





    3. Determine the quadrants in which the angle is found, here it is in the first and second quadrant, where sine is both positive.

    4. Equate to your obtained angles, you'll have



    5. Finally solve for theta, you'll have 15 and 75 in degrees.

  • Apr 26, 2009, 08:53 PM
    Perito
    Quote:

    Originally Posted by sdlinsey View Post



    so

  • Apr 27, 2009, 10:41 AM
    Unknown008

    Oh, sorry, I couldn't possibly know at what level of Mathematics you are... Perito gave the answer anyway...

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