# Query

• May 8th 2012, 04:26 PM
bigtumbler
Query
Where possible find all angles between 0 and 2(pi) that satisy the equation?

cot^2(theta)+5 = 6cot(theta)

I got theta = (pi)/4 radians and 3.927 radians.

Is this correct or are there other solutions?

Apologies for poor formatting. Unsure how to do otherwise. Theta = angle.

Many thanks

Simon

• May 8th 2012, 04:57 PM
skeeter
Re: Query
Quote:

Originally Posted by bigtumbler
Where possible find all angles between 0 and 2(pi) that satisy the equation?

cot^2(theta)+5 = 6cot(theta)

I got theta = (pi)/4 radians and 3.927 radians.

Is this correct or are there other solutions?

Apologies for poor formatting. Unsure how to do otherwise. Theta = angle.

Many thanks

Simon

$\cot^2{\theta} - 6\cot{\theta} + 5 = 0$

$(\cot{\theta} - 1)(\cot{\theta} - 5) = 0$

$\cot{\theta} = 1$

$\theta = \frac{\pi}{4} , \frac{5\pi}{4}$

$\cot{\theta} = 5$

$\theta = \cot^{-1}(5) = .197 \, , \, \pi + \cot^{-1}(5) = 3.339$