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NDA 2016 Maths · Mathematics · Trigonometric Functions and Identities · medium

The value of sin (-765^°) is

Single correct option

The value of sin⁡(−765∘)\sin(-765^\circ) is
  1. A. 12\dfrac1{\sqrt2}
  2. B. −32-\dfrac{\sqrt3}2
  3. C. −12-\dfrac1{\sqrt2}
  4. D. 12\dfrac12
Show answer and solution

Answer: (C) −12-\dfrac1{\sqrt2}

Sine is odd, so sin⁡(−765∘)=−sin⁡765∘\sin(-765^\circ)=-\sin765^\circ. Subtract two full turns: 765∘−720∘=45∘765^\circ-720^\circ=45^\circ, so sin⁡765∘=12\sin765^\circ=\dfrac1{\sqrt2}. Therefore the value is −12-\dfrac1{\sqrt2}. Ignoring the odd property gives the wrong sign.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake