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satellite73
find sin(x) if cot(x)=-4
Lol...@satellite73 r u alright ?
Find sin θ if cot θ = –4 and cos θ < 0.
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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 \(\frac{4}{1}=4\)
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
\[(sin^2 + cos^2 = 1)/sin^2\] \[1 + cot^2 = csc^2\] \[1 + (-4)^2 = csc^2\] \[17 = csc^2\] \[\sqrt{17} = csc\] \[\frac{\sqrt{17}}{17} = sin\]
maybe do a +- for the sqrt to account for a quadrant
\[\frac{1}{\sqrt{17}}=\frac{1}{\sqrt{17}}\times \frac{\sqrt{17}}{\sqrt{17}}=\frac{\sqrt{17}}{17}\]