# Find the principal solutions of sin x = -12 - Mathematics and Statistics

Sum

Find the principal solutions of sin x = -1/2

#### Solution

sin x = -1/2

∴ sin x = −sin (pi/6)

∴ sin x = sin (pi + pi/6)

= sin ((7pi)/6) ans sin x = sin (2pi - pi/6)

= sin((11pi)/6)

such that 0 ≤ (7pi)/6 < 2pi and 0 ≤ (11pi)/6 < 2pi

∴ The required principal solutions are x = (7pi)/6 and x = (11pi)/6.

Concept: Trigonometric Equations and Their Solutions
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