# Math Help - Trigonometric Equation

1. ## Trigonometric Equation

Solve the equation between $0 \leq \theta \leq 360$ for
$tan^2\theta + 2sec\theta = 7$

$\theta$ = 60, 300, 104.5, 244.5.
Are these values correct? I am new to these trigonometric identities and if I have this right then it's definitely a step in the right direction.
If not, then I'll post my working to try and find out where I went wrong.
Thanks if you can help

2. Hello, db5vry!

Except for a bit of arithmetic, good work!

My answers for this: $\theta \:= \:60^o,\;300^o,\;104.5^o,\;{\color{red}\rlap{/////}}244.5^o$

That last angle should be: $255.5^o$

3. $tan^2\theta + 2sec\theta = 7$

$(* by cos^2\theta):sin^2\theta+2cos\theta=7cos^2\theta$
$8cos^2\theta-2cos\theta-1=0$
$(4cos\theta+1)(2cos\theta-1)=0$
$cos\theta=-0.25,+0.5$

$\theta=60,300,104.478,255.522$