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Math Help - Trig

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    Trig

    An angle, x, lies in the fourth quadrant and sinx=-1/3. Find the five remaining trigonometric ratios of x without finding x first.

    Could someone please explain how to go about solving this? I dont understand the question at all. I think you use the CAST diagram? If so, how would you use it? I've never used it before. Cheers.
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  2. #2
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    Quote Originally Posted by Haris View Post
    An angle, x, lies in the fourth quadrant and sinx=-1/3. Find the five remaining trigonometric ratios of x without finding x first.

    Could someone please explain how to go about solving this? I dont understand the question at all. I think you use the CAST diagram? If so, how would you use it? I've never used it before. Cheers.
    \sin X =\frac{y}{r}=\frac{-1}{3}

    y = -1 and r = 3

    Use the Pythagorean theorem to find x.

    r^2=x^2+y^2

    9=x^2+1

    x^2=8

    x=2\sqrt{2}

    Now substitute these values into the remaining trig ratios.

    \cos X=\frac{x}{r} \ \ \ \ \ \ \sec X = \frac{r}{x}

    \tan X=\frac{y}{x} \ \ \ \ \ \ \cot X = \frac{x}{y}

    \csc X= \frac{r}{y}=\frac{3}{-1}=-3
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