Unit circle: cos⁻¹(−½) = 2π/3इकाई वृत्त: cos⁻¹(−½) = 2π/3Unit circle: cos⁻¹(−½) = 2π/3

NCERT Exercise 2.1 · Class 12 Maths · Chapter 2 · interactive diagram

Parts and what they mean

• Unit circle (radius 1) (इकाई वृत्त (त्रिज्या 1)) — A point at angle θ on it is (\cos\theta, \sin\theta): x-coordinate = cos, y-coordinate = sin.
• x-axis (cos values) (x-अक्ष (cos के मान)) — The x-coordinate of a point on the circle is \cos\theta.
• y-axis (sin values) (y-अक्ष (sin के मान)) — The y-coordinate of a point on the circle is \sin\theta.
• Centre O (केंद्र O) — Angles are measured from the positive x-axis, anticlockwise = positive.
• The \cos^{-1} zone: [0, \pi] (\cos^{-1} क्षेत्र: [0, \pi]) — The upper half of the circle (0° to 180°). Every value of \cos^{-1} is an angle here — never negative.
• Line x = -\tfrac12 (रेखा x = -\tfrac12) — All angles with \cos\theta = -\frac12 sit where this line meets the circle.
• \theta = 2\pi/3 (120°) — inside (\theta = 2\pi/3 (120°) — अंदर) — \cos^{-1}(-\frac12) = \pi - \frac{\pi}{3} = \frac{2\pi}{3}.
• \theta = -2\pi/3 — outside (\theta = -2\pi/3 — बाहर) — Same cosine, but negative angles are not in [0, \pi]. A common wrong answer is -\pi/3.
• Angle 120° = 2π/3 (कोण 120° = 2π/3) — Measured anticlockwise from the positive x-axis.

Original diagram drawn by Simple Learning Hub, based on NCERT Exercise 2.1. Report a mistake