# Trig angles

• Jan 29th 2009, 08:03 AM
Haris
Trig angles
How many solutions are there to the equation tan(x) = 2 in the interval [http://ta2.maths.ed.ac.uk:8080/maple...cljnecnmig.gif, http://ta2.maths.ed.ac.uk:8080/maple...dobgnoifeg.gif].

How would you solve this? Cheers.
• Jan 29th 2009, 08:24 AM
metlx
[http://ta2.maths.ed.ac.uk:8080/maple...cljnecnmig.gif, http://ta2.maths.ed.ac.uk:8080/maple...dobgnoifeg.gif] = $[-540^0 , 540^0]$

$
tan x = 2 \Rightarrow x = 63.43^0 \pm k\Pi
$

$
x_{1} = 63.43^0 - 3\Pi = -476.57^0
$

$
x_{2} = 63.43^0 - 2\Pi = -296.57^0
$

$
x_{3} = 63.43^0 - \Pi = -116.57^0
$

$
x_{4} = 63.43^0
$

$
x_{5} = 63.43^0 + \Pi = 243.43^0
$

$
x_{6} = 63.43^0 + 2\Pi = 423.43^0
$