Question

find sin(x) if cot(x)=-4

Answer 1

Lol...@satellite73 r u alright ?

Answer 2

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

Answer 3

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 \(\frac{4}{1}=4\)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

\[\frac{1}{\sqrt{17}}=\frac{1}{\sqrt{17}}\times \frac{\sqrt{17}}{\sqrt{17}}=\frac{\sqrt{17}}{17}\]