Find all values of theta in the interval [0°,360°) that have the given function value.

Question

tan theta = √3/3

 

Answer 1

Let x=theta

 

tanx = √(3) / 3

 

x = tan^-1[√(3)/3]

 

 

Since tangent is positive in the 1st and 3rd quadrants,

 

x = 180° + tan^-1[√(3)/3]

Answer 2

The trigonometric values of the 30-60-90 triangle are very useful. Memorize them!

tan θ = √3 / 3

θ = π/6, 5π/6