JEE Main 2022 · Mathematics · Trigonometry and Inverse Trigonometric Functions · medium

How many values of x in the closed interval [0,2π] satisfy the equation sin 2x=1/2?

Single correct option

How many values of

x

in the closed interval

[0,2\pi]

satisfy the equation

\sin 2x=\dfrac12

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Answer: (D) $4$

Let

\theta=2x

, which ranges over

[0,4\pi]

. In each period of

2\pi

\sin\theta=\frac12

has two solutions (

\theta=\frac\pi6,\frac{5\pi}6

). Two periods give 4 solutions:

\theta=\frac\pi6,\frac{5\pi}6,\frac{13\pi}6,\frac{17\pi}6

, i.e.

x=\frac\pi{12},\frac{5\pi}{12},\frac{13\pi}{12},\frac{17\pi}{12}

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