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If 4 sin2 θ = 3, then θ = ?
1. 145
2. 150
3. 240
4. 180° 

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Correct Answer - Option 3 : 240

Concept:

Values of Trigonometric Ratios for Common Angles:
 

30°

45°

60°

90°

sin

0

\(\frac{1}{2}\)

\(\frac{1}{\sqrt2}\)

\(\frac{\sqrt3}{2}\)

1

cos

1

\(\frac{\sqrt3}{2}\)

\(\frac{1}{\sqrt2}\)

\(\frac{1}{2}\)

0

tan

0

\(\frac{1}{\sqrt3}\)

1

√3

csc

2

√2

\(\frac{2}{\sqrt3}\)

1

sec

1

\(\frac{1}{\sqrt3}\)

√2

2

cot

√3

1

\(\frac{1}{\sqrt3}\)

0

 

Trigonometric Ratios for Allied Angles: 

  • sin (-θ) = -sin θ.
  • cos (-θ) = cos θ.
  • sin (2nπ + θ) = sin θ.
  • cos (2nπ + θ) = cos θ.
  • sin (nπ + θ) = (-1)n sin θ.
  • cos (nπ + θ) = (-1)n cos θ.
  • \(\rm \sin \left [(2n+1)\frac{\pi}{2}+θ \right ]\) = (-1)n cos θ.
  • \(\rm \cos \left [(2n+1)\frac{\pi}{2}+θ \right ]\) = (-1)n (-sin θ).


Calculation:

4 sin2 θ = 3

⇒ sin θ = \(\pm\frac{\sqrt3}{2}\)

From the table of the values of trigonometric ratios, we get:

θ = 60 OR -60

Since sin (π + θ) = -sin θ, we get:

⇒ θ = 60 OR 180 + 60 = 240

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