Maharashtra State BoardHSC Arts 12th Board Exam
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Find the principal solutions of sin x = -12 - Mathematics and Statistics

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Sum

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

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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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