NCERT · Class 11 · Mathematics · Trigonometric FunctionsFind the value of $\sin\left(765^{\circ}\right)$.
Step-by-Step Solution
We can write $\sin(765^{\circ}) = \sin(2 \times 360^{\circ} + 45^{\circ})$. Since trigonometric functions repeat their values after an interval of $360^{\circ}$ (or $2\pi$), $\sin(2 \times 360^{\circ} + 45^{\circ}) = \sin(45^{\circ}) = \frac{1}{\sqrt{2}}$.
Detailed Options Breakdown
Option : \frac{1}{2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.
Option 1: \frac{1}{\sqrt{2}} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: \frac{\sqrt{3}}{2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.
Option 3: 1
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.