What is the radian measure of 150°?

Question

What is the radian measure of 150°?

1. A. \(5π/6\) (Correct answer)
2. B. \(2π/3\)
3. C. \(3π/4\)
4. D. \(π/3\)

Correct Answer

Option A — \(5π/6\)

Detailed Solution & Explanation

The correct answer is 5π/6.

Key Points

• Convert degrees to radians by multiplying by π/180:
  • 150 × π/180 = 150π/180
• Divide numerator and denominator by 30: 5π/6.

Additional Information

• The conversions worth memorising outright: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 120° = 2π/3, 135° = 3π/4, 150° = 5π/6, 180° = π, 270° = 3π/2, 360° = 2π.
• Going the other way, multiply radians by 180/π.
• A quick sanity check: 150° is between 90° (π/2 = 3π/6) and 180° (π = 6π/6), so the answer must lie between 3π/6 and 6π/6 — which 5π/6 does, while 2π/3 = 4π/6 corresponds to 120° and π/3 to 60°.
• Radians are the natural measure of angle in higher mathematics because arc length is simply rθ and sector area ½r²θ, with no conversion factor.
• One radian is the angle subtending an arc equal in length to the radius, so a full circle is 2π radians ≈ 6.283, making one radian roughly 57.3°.

प्रश्न (हिन्दी में)

150° का रेडियन माप क्या है?

1. A. \(5π/6\)
2. B. \(2π/3\)
3. C. \(3π/4\)
4. D. \(π/3\)