Find the principal solutions of sin x = -12 - Mathematics and Statistics
Find the principal solutions of sin x = `-1/2`
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)`
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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