MP Board Class 11 Mathematics — What is the value of $\sin

MP Board · Class 11 · Mathematics · Trigonometric FunctionsWhat is the value of $\sin\left(-\frac{11\pi}{3}\right)$?

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Total Attempts: 2

Accuracy Rate: 50%

Step-by-Step Solution

We know that $\sin(-\theta) = -\sin(\theta)$. So, $\sin\left(-\frac{11\pi}{3}\right) = -\sin\left(\frac{11\pi}{3}\right)$. We can write $\frac{11\pi}{3} = 4\pi - \frac{\pi}{3}$. Thus, $-\sin\left(4\pi - \frac{\pi}{3}\right) = -\left(-\sin\left(\frac{\pi}{3}\right)\right) = \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$.

Detailed Options Breakdown

Option : -\frac{\sqrt{3}}{2}

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

Option 1: \frac{\sqrt{3}}{2} (Correct Answer)

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

Option 2: -\frac{1}{2}

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

Option 3: \frac{1}{2}

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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