How do I solve goniometric inequations with cosine and tangent?

[scientifico]

Hello, how can I solve cos(7x) > cos(3x) and tan(x) > -3 ?

I know in the second one x is greater than -arctan(3) but smaller than what?

Thanks!

 

[tiny-tim]

hi scientifico!

arctan(∞) ?

 

[scientifico]

90° + k*180°

 

[tiny-tim]

yes

(and of course you'll need the same " + k*180° " for arctan(-3) )

 

[scientifico]

x < -arctan(3) + k*180° ?

 

[tiny-tim]

that makes no sense

you can't have one equation (or inequation) with a multiple-value k !

 

[scientifico]

270°+ k*180° < x < -arctan(3) + k*180°