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.

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- Mar 18th 2010, 11:06 PMsomanyquestions[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 AMGrandad
Hello somanyquestionsYou need to use Pythagoras' Theorem to find the length of the third side:

$\displaystyle \cot s = \frac{\text{Adjacent}}{\text{Opposite}}$So we can now say:$\displaystyle = (-)\frac{1}{3}$ (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$$\displaystyle \Rightarrow\text{Hypotenuse}=\sqrt{10}$$\displaystyle \sin s = \pm\frac{\text{Opposite}}{\text{Hypotenuse}}$Now we can look at the sign of sine in QIV (as you correctly did), and say:$\displaystyle =\pm\frac{3}{\sqrt{10}}$$\displaystyle \sin s = -\frac{3}{\sqrt{10}}$Grandad - Mar 19th 2010, 09:05 AMrasczak
Wow, Thanks! You've made this a lot clearer for me. :)