# Thread: How to solve trig equations - is it ok to take values off graph

1. ## How to solve trig equations - is it ok to take values off graph

Hello

I am studying A level maths A2 in UK. So level is pre-University maths.

I have for example, this equation to solve for 0 <= x <= 360.

cosec x = sec x.

I am solving like this:

$\frac{1}{sin x} = \frac{1}{cos x}$

$sin x = cos x$

x = 45 and 225 degrees.

Then looking on a graph of sin and cos x to see where they intersect. Is that the way to do it? Or is there a more rigorous method? Is there an algebraic method?

Angus

2. ## Re: How to solve trig equations - is it ok to take values off graph

$\sin x = \cos x \Rightarrow \tan x= 1 \Rightarrow x_1 = \frac{\pi}{4} , x_2=\frac{5\pi}{4}$

3. ## Re: How to solve trig equations - is it ok to take values off graph

for completeness you could also check that there are no solutions where sinx=cosx=0 (this is in fact the case)