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Math Help - [SOLVED] description question about reference angles.

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    [SOLVED] description question about reference angles.

    Explain how the reference angle is used to find values of the trigonometric functions for an angle in quadrant III.

    ?? i don't know.
    and also, why is the reference angle always found with reference to the x-axis and not the y-axis?
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  2. #2
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    Hello somanyquestions
    Quote Originally Posted by somanyquestions View Post
    Explain how the reference angle is used to find values of the trigonometric functions for an angle in quadrant III.

    ?? i don't know.
    and also, why is the reference angle always found with reference to the x-axis and not the y-axis?
    The reference angle is always measured anti-clockwise from the positive direction of the x-axis.

    Your question about why not the y-axis is pointless. A definition is a definition. You may define a different reference angle starting from the y-axis if you wish - or indeed any other line - but in doing so, you will be creating a different definition. You might as well ask "Why doesn't the alphabet start at the letter 'n'?". Without some agreed conventions, we should get nowhere.

    OK then. If the point (x, y) is on the unit circle, and the radius joining (0, 0) to (x,y) makes an angle \theta with the positive direction of the x-axis, measured anticlockwise, as described above, then, by definition:
    \left\{\begin{array}{l}<br />
\cos\theta = x\\<br />
\sin\theta = y\\<br />
\end{array}\right.
    This definition holds good for all values of \theta; i.e. for angles in all quadrants. In particular, in QIII, where x<0 and y<0, this will mean that \cos\theta and \sin\theta are both negative.

    Draw a diagram, showing an angle \theta between \pi and 3\pi/2 (i.e. (x,y) lies in QIII). Now draw the diameter through (x,y) to meet the circle again in QI. You should be able to see that this shows that:
    \left\{\begin{array}{l}<br />
\cos\theta = - \cos(\theta-\pi)\\<br />
\sin\theta = -\sin(\theta-\pi)\\<br />
\end{array}\right.
    where 0 < (\theta - \pi) < \pi/2; i.e. (\theta - \pi) is an acute angle. This shows how to relate the values of sine and cosine in QIII to those in QI.

    Grandad
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