## satellite73 2 years ago find sin(x) if cot(x)=-4

1. Yahoo!

Lol...@satellite73 r u alright ?

2. sara1234

Find sin θ if cot θ = –4 and cos θ < 0.

3. satellite73

|dw:1352819529461:dw|

4. satellite73

first we forget about the minus sign, we will worry about that later i just drew a right triangle with the "adjacent side" of 4 and the "opposite side" of 1 because $$\frac{4}{1}=4$$

5. satellite73

what is missing is the hypotenuse, and we find that by pythagoras $h^2=1^2+4^2$ $h^2=17$ $h=\sqrt{17}$ now we can finish labelling the triangle

6. amistre64

$(sin^2 + cos^2 = 1)/sin^2$ $1 + cot^2 = csc^2$ $1 + (-4)^2 = csc^2$ $17 = csc^2$ $\sqrt{17} = csc$ $\frac{\sqrt{17}}{17} = sin$

7. amistre64

maybe do a +- for the sqrt to account for a quadrant

8. satellite73

$\frac{1}{\sqrt{17}}=\frac{1}{\sqrt{17}}\times \frac{\sqrt{17}}{\sqrt{17}}=\frac{\sqrt{17}}{17}$