Find all the angles between -π and π with basic angle α = π /18. ?

Question

give explanation too if possible.

Answer 1

I don't know what this question means.  If we had solved an equation

sin x = ...

and the acute value of x turned out to be α = π/18,

then the other solution in this range would be

x = π - α

.. = 17π / 18

I wonder if your question really means what are all the angles for which the acute angle between the radius and the x axis is π/18?

If so, the answer is -17π/18, -π/18, π/18, 17π/18.

If we were solving cos x = cos π/18, the solutions would be the middle two values,

-π/18 and π/18

To solve tan x = tan π/18, the solutions are in the first and third quadrants, so we would get

x = -17π/18, π/18.