The general value of \\theta, satisfying the equations, \tan \\theta={1}/{\\sqrt{3} and \sin \\theta=\frac{-1}{2} is

Correct Answer is : θ=2nπ+7π6,n∈I

\\theta=n \\pi+\frac{\\pi}{6}, n \\inI

n \\pi+(-1)^{n}(\frac{7 \\pi}{6}), n \\in\I

\\theta=2 n \\pi\+\frac{7 \\pi}{6}, n \\inI

\\theta=2 n \\pi\\pm\frac{11 \\pi}{6}, n \\in\I

NIMCET 2021 Question Paper with solutions

Question : 17 of 120

Marks: +1, -0

The general value of

\θ

, satisfying the equations,

\tan \θ={1}/{\√{3}}

and

\sin \θ={-1}/{2}

Solution:

\tan \θ={1}/{\√{3}}

and

\sin \θ={-1}/{2}

\⇒\θ=\{-{\π}/{6}, 2 \π-{\π}/{6}, \π+{\π}/{6}\} \∩\{{\π}/{6}, \π+{\π}/{6}\}

\⇒\θ=\{-{\π}/{6}, {11 \π}/{6}, {7 \π}/{6} \} \∩\{{\π}/{6}, {7 \π}/{6}\}

⇒\θ=2 n \π\+{7 \π}/{6}, n \∈I

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