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Thread: reference angles

  1. #1
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    reference angles

    Hi;
    Need help with reference angles... I know the cos of 150degrees and the cos of 30degrees are the same ie sqrt3 /2 but with a sign change.

    I know they lie in the same quadrant but that all I know and I need to be able to prove it.

    Thanks
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  2. #2
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    Re: reference angles

    Unfortunately, what you say you "know" is wrong. "150 degrees" lies between 90 and 180 so is in the second quadrant while 30 degrees is between 0 and 90 degrees and, like any "reference angle", is in the first quadrant. Are you clear on what "quadrant" means here? Representing points on a unit circle, in an xy-coordinate system, the "quadrants" are the four parts into which the x and y axes divide the plane. The "first quadrant" is the upper right, between 0 and 90 degrees where x and y are both positive. Since "sine" is the y coordinate on the unit circle and "cosine" is the x coordinate, they are both positive in the first quadrant. The "second quadrant" is the upper left, between 90 and 180 degrees where x is negative and y is positive- sine is still positive but now cosine is negative. The "third quadrant" is the lower left, between 180 and 270 degrees where x and y are both negative so sine and cosine are both negative. Finally, the "fourth quadrant" is the lower right, between 270 and 360 degrees where x is positive and y is negative. Cosine is positive and sine is negative. As you go through the four quadrants, from first to fourth, sine goes "+,+,-,-" while cosine goes "+,-,-,+".
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  3. #3
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    Re: reference angles

    Yeah I meant the reference angle lies in the second quadrant where the terminal side of 150dgree lies
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