# Find the principal solutions of tan x = -3 - Mathematics and Statistics

Sum

Find the principal solutions of tan x = -sqrt(3)

#### Solution

tan x = -sqrt(3)

∴ tan x = -tan (pi/3)

∴ tan x = tan (pi - pi/3)

= tan ((2pi)/3) and  tan x = tan (2pi - pi/3)

= tan ((5pi)/3)

such that 0 ≤ (2pi)/3 < 2pi and 0 ≤ (5pi)/3 < 2pi

∴ The required principal solutions are x = (2pi)/3 and x = (5pi)/3.

Concept: Trigonometric Equations and Their Solutions
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