Thread: Trig angles

How many solutions are there to the equation tan(x) = 2 in the interval [, ].

How would you solve this? Cheers.

[, ] = $\displaystyle [-540^0 , 540^0]$

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

$\displaystyle
x_{1} = 63.43^0 - 3\Pi = -476.57^0
$
$\displaystyle
x_{2} = 63.43^0 - 2\Pi = -296.57^0
$
$\displaystyle
x_{3} = 63.43^0 - \Pi = -116.57^0
$
$\displaystyle
x_{4} = 63.43^0
$
$\displaystyle
x_{5} = 63.43^0 + \Pi = 243.43^0
$
$\displaystyle
x_{6} = 63.43^0 + 2\Pi = 423.43^0
$