What is 5π/4 radians in degrees?

Question

What is 5π/4 radians in degrees?

1. A. 225° (Correct answer)
2. B. 180°
3. C. 240°
4. D. 360°

Correct Answer

Option A — 225°

Detailed Solution & Explanation

The correct answer is 225°.

Key Points

• Convert with 180° = π radians, so multiply by $\dfrac{180}{\pi}$.
• $\dfrac{5\pi}{4} \times \dfrac{180}{\pi} = \dfrac{5 \times 180}{4} = 225°$.

Additional Information

• The π cancels, which is why radian-to-degree conversions of the form $k\pi$ are always exact.
• Common equivalents worth memorising: $\pi/6 = 30°$, $\pi/4 = 45°$, $\pi/3 = 60°$, $\pi/2 = 90°$, $\pi = 180°$, $2\pi = 360°$.
• 225° lies in the third quadrant, where sine and cosine are both negative and tangent is positive.

प्रश्न (हिन्दी में)

5π/4 रेडियन कितने डिग्री में है?

1. A. 225°
2. B. 180°
3. C. 240°
4. D. 360°