# [SOLVED] finding sin s

• Mar 18th 2010, 11:06 PM
somanyquestions
[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.
• Mar 19th 2010, 12:42 AM
Hello somanyquestions
Quote:

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:
$\cot s = \frac{\text{Adjacent}}{\text{Opposite}}$
$= (-)\frac{1}{3}$ (I've put the minus sign in brackets, because at this stage we don't need to worry about it.)
$\Rightarrow \text{Hypotenuse}^2 = 1^2+3^2$
$=10$
$\Rightarrow\text{Hypotenuse}=\sqrt{10}$
So we can now say:
$\sin s = \pm\frac{\text{Opposite}}{\text{Hypotenuse}}$
$=\pm\frac{3}{\sqrt{10}}$
Now we can look at the sign of sine in QIV (as you correctly did), and say:
$\sin s = -\frac{3}{\sqrt{10}}$