anonymous
  • anonymous
Find cot θ if csc θ = square root 5 / 2 and tan θ > 0
Mathematics
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\csc \theta~is~positive.~so~\theta ~lies~\in~1st~and~2rd~quadrant.\] \[\tan \theta>0,~so~\theta~lies~\in~1st~and~3rd~quadrant.\ Hence cot theta is positive. \[\csc ^2\theta-\cot ^2\theta=1\] find cot theta
triciaal
  • triciaal
|dw:1434926766237:dw|
anonymous
  • anonymous
\[\csc ^2 \theta-\cot ^2 \theta=1\]

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triciaal
  • triciaal
|dw:1434926958761:dw|
anonymous
  • anonymous
soo cot theta = 2 @triciaal @surjithayer
triciaal
  • triciaal
|dw:1434928410796:dw|
triciaal
  • triciaal
sin = opposite / hypotenuse so csc = hypotenuse/ opposite given as rt 5/ 2 cot = 1/tan = adjacent/ hypotenuse
anonymous
  • anonymous
ohh okay thank you @triciaal
triciaal
  • triciaal
****tan = opposite/ adjacent so cot = adjacent/opposite not hypotenuse
triciaal
  • triciaal
welcome
anonymous
  • anonymous
\[\left( \frac{ \sqrt{5} }{ 2 } \right)^2-\cot ^2 \theta=1\] \[\cot ^2 \theta=\frac{ 5 }{ 4 }-1=\frac{ 5-4 }{ 4 }=\frac{ 1 }{ 4 }\] \[\cot \theta=\pm \frac{ 1 }{ 2 }\] but cot theta>0 hence cot theta=?

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