What is principle value in trigonometry?

Answer 1

The trigonometric functions: sine, cosine, tan as well as their reciprocals are periodic so that their value repeats every 2Ï€ radians. As a result, the inverse operations are functions only over restricted domains, as follows.

Sine : −π/2 ≤ y ≤ π/2

Cosine: 0 ≤ y ≤ π

Tangent: −π/2 < y < π/2

The principal value is the angle that lies within the relevant range. All other solutions are non-principal.

Similarly, the principal square root of a positive real number is the positive square root. The negative root is not the principal root.