Question

How do you solve cosx=0?

Answer 1

`x=pi/2+kpi, k in ZZ`

Explanation:

In the trigonometric circle you will notice that cos(x)=0 corresponds to `x=pi/2` and also `x=-pi/2`. Additionally to these all the angles that make a complete turn of the circle (`2kpi`) plus `+-pi/2` correspond to cos(x)=0. So you have:

`x=+-pi/2+2kpi, k in ZZ`

If you try to see which are the first elements (from k =0, 1,2...of this series you will find that they are:

`-pi/2;pi/2; (3pi)/2; (5pi)/2; (7pi)/2....`, which can be described by:

`x=pi/2+kpi, k in ZZ`