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Mathematics

Trigonometric equations

In this Class 12 Mathematics topic from the chapter Trigonometric Functions, students learn how to solve equations involving sine, cosine, tangent and their combinations. They use trigonometric identities, standard angles, periodicity and the general solutions of basic equations to find all valid values of the variable. The topic also develops careful handling of solution intervals, equivalent forms and verification, helping students connect algebraic methods with the graphs and properties of trigonometric functions.

Medium · Level 1 · 1 questions

Practice questions

01If sin x = 1/2, what are the values of x in 0 ≤ x < 2π?

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Answer and explanation

Correct answer: A. π/6, 5π/6

This is a trigonometric-equation problem on one complete interval. The reference angle for sin x = 1/2 is π/6 because sin(π/6) = 1/2. Sine is positive in the first and second quadrants, so the solutions in 0 ≤ x < 2π are π/6 and π − π/6 = 5π/6. Thus option A is correct. Option B uses π/3, but sin(π/3) = √3/2 rather than 1/2. The angle 7π/6 in option C lies in the third quadrant, where sine is negative. Option D also includes third-quadrant 7π/6 and omits the first-quadrant solution, so it cannot satisfy the equation.

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Trigonometric equations

Practice questions

01If sin x = 1/2, what are the values of x in 0 ≤ x < 2π?यदि sin x = 1/2 है, तो 0 ≤ x < 2π में x के मान क्या होंगे?

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01If sin x = 1/2, what are the values of x in 0 ≤ x < 2π?