# Thread: [SOLVED] finding sin s

1. ## [SOLVED] finding sin s

cot s = -1/3, s in quadrant IV
what is sin s in quadrant IV?

well..
cot s= cos s/sin s
since it's quadrant IV, cos is + and sin is -
-1/3 = 1/-3
sin s= -3

is this correct? i think i'm doing it right.

2. Hello somanyquestions
Originally Posted by somanyquestions
cot s = -1/3, s in quadrant IV
what is sin s in quadrant IV?

well..
cot s= cos s/sin s
since it's quadrant IV, cos is + and sin is -
-1/3 = 1/-3
sin s= -3

is this correct? i think i'm doing it right.
You need to use Pythagoras' Theorem to find the length of the third side:
$\displaystyle \cot s = \frac{\text{Adjacent}}{\text{Opposite}}$
$\displaystyle = (-)\frac{1}{3}$ (I've put the minus sign in brackets, because at this stage we don't need to worry about it.)
$\displaystyle \Rightarrow \text{Hypotenuse}^2 = 1^2+3^2$
$\displaystyle =10$
$\displaystyle \Rightarrow\text{Hypotenuse}=\sqrt{10}$
So we can now say:
$\displaystyle \sin s = \pm\frac{\text{Opposite}}{\text{Hypotenuse}}$
$\displaystyle =\pm\frac{3}{\sqrt{10}}$
Now we can look at the sign of sine in QIV (as you correctly did), and say:
$\displaystyle \sin s = -\frac{3}{\sqrt{10}}$