1. ## 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.

2. Originally Posted by Haris
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.
$\displaystyle \sin X =\frac{y}{r}=\frac{-1}{3}$

y = -1 and r = 3

Use the Pythagorean theorem to find x.

$\displaystyle r^2=x^2+y^2$

$\displaystyle 9=x^2+1$

$\displaystyle x^2=8$

$\displaystyle x=2\sqrt{2}$

Now substitute these values into the remaining trig ratios.

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

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

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