satellite73
  • satellite73
find sin(x) if cot(x)=-4
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Lol...@satellite73 r u alright ?
anonymous
  • anonymous
Find sin θ if cot θ = –4 and cos θ < 0.
anonymous
  • anonymous
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anonymous
  • anonymous
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 \(\frac{4}{1}=4\)
anonymous
  • anonymous
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
amistre64
  • amistre64
\[(sin^2 + cos^2 = 1)/sin^2\] \[1 + cot^2 = csc^2\] \[1 + (-4)^2 = csc^2\] \[17 = csc^2\] \[\sqrt{17} = csc\] \[\frac{\sqrt{17}}{17} = sin\]
amistre64
  • amistre64
maybe do a +- for the sqrt to account for a quadrant
anonymous
  • anonymous
\[\frac{1}{\sqrt{17}}=\frac{1}{\sqrt{17}}\times \frac{\sqrt{17}}{\sqrt{17}}=\frac{\sqrt{17}}{17}\]

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