If sin θ = - 1/2 and tan θ = 1/{3} , then θ =

Correct Answer is : 2nπ + 7π/6

Correct Answer is : 2nπ + 7π/6

Test Index

BITSAT 2011 Paper

Section: Mathematics

Question : 83 of 150

Marks: +1, -0

If sin θ = -

\frac{1}{2}

\sqrt{3}

, then θ =

Solution:

We shall first consider values of θ between 0 and 2π sin θ =

\frac{1}{2}

= - sin

\frac{\pi}{6}

= sin

\left(\pi + \frac{\pi}{6}\right)

or sin (2π – π/6)

∴ θ = 7π/6 ; 11π/6

tan θ = 1/

\sqrt{3}

= tan (π/6) or tan (π + π/6)

∴ θ = π/6 , 7π/6

The value of θ which satisfies both the equations is 7π/6

Hence the general value of θ is 2nπ + 7π/6 where n ∊ I

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