Give the exact value of x. cot3x=square root of 3

Question

I am supposed to write the question in radians. It is in the range of [0,2pi)

Answer 1

cot(3x)=√3, tan(3x)=1/√3, 3x=π/6 (30°), because tan30°=1/√3=cot60°.

Therefore 3x=30°, x=10° or π/18.

Also, 3x=210°(π+π/6=7π/6), x=70° (7π/18).

The general answer is (πn+π/6)/3 or ⅓(n+⅙)π radians, that is, 60(n+⅙)°=60°n+10°, where n is an integer.