NIMCET 2021 — Mathematics PYQ

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Question

NIMCET 2021 — Mathematics PYQ

NIMCET | Mathematics | 2021

The general value of $θ$ , satisfying the equations $sin θ = - \frac{1}{2}$ and $tan θ = \frac{1}{3}$ is:

Choose the correct answer:

Explanation

Solution

1. Identifying the Quadrant

$\sin \theta = -\frac{1}{2} < 0$ (Negative)

$\tan \theta = \frac{1}{\sqrt{3}} > 0$ (Positive)

Sine negative aur Tangent positive sirf Third Quadrant me hote hain.

2. Principal Value Calculation

Basic angle $α = \frac{π}{6}$ (kyunki $sin \frac{π}{6} = \frac{1}{2}$ ).

Third quadrant ke liye:

$θ = π + α = π + \frac{π}{6} = \frac{7 π}{6}$

3. General Solution

Jab do trigonometric equations ko ek saath satisfy karna ho, toh general solution $2 nπ$ ke period ke saath likha jata hai:

$θ = 2 nπ + \frac{7 π}{6}$

Correct Option: (b) $2 nπ + \frac{7 π}{6}$