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CBSE · Class 11 · Mathematics · Trigonometric FunctionsConvert $40^{\circ} 20'$ into radian measure.

Step-by-Step Solution

We know that $1^{\circ} = 60'$. Therefore, $20' = \frac{20}{60}^{\circ} = \left(\frac{1}{3}\right)^{\circ}$. Thus, $40^{\circ} 20' = 40\frac{1}{3}^{\circ} = \frac{121}{3}^{\circ}$. To convert degrees to radians, we multiply by $\frac{\pi}{180}$. So, $\frac{121}{3} \times \frac{\pi}{180} = \frac{121\pi}{540}$ radians.

Detailed Options Breakdown
Option : $\frac{121\pi}{540}$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 1: $\frac{121\pi}{180}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.

Option 2: $\frac{\pi}{180}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.

Option 3: $\frac{40\pi}{3}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.

💡 Study Guide: This question tests core syllabus concepts from Trigonometric Functions. For formulas, key summaries, and mock exam reference guides, read the full Trigonometric Functions Revision Notes.
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