Unit circle: cos x and sin x, and signs in the four quadrantsइकाई वृत्त: cos x और sin x, तथा चारों चतुर्थांशों में चिह्नUnit circle: cos x aur sin x, aur chaaron quadrants mein signs
Fig 3.6 · Class 11 Maths Ch 3 · interactive diagram
Parts and what they mean
- Unit circle (radius 1) (इकाई वृत्त (त्रिज्या 1)) — Centre at the origin, radius 1. So for every point on it, cos²x + sin²x = 1.
- Point P(cos x, sin x) (बिंदु P(cos x, sin x)) — P is reached by turning through arc length x from (1, 0). Its coordinates define cos x and sin x for ANY angle.
- cos x = x-coordinate of P (cos x = P का x-निर्देशांक) — Positive on the right half (quadrants I, IV), negative on the left half.
- sin x = y-coordinate of P (sin x = P का y-निर्देशांक) — Positive in the upper half (quadrants I, II), negative in the lower half.
- Angle x (radians) (कोण x (रेडियन)) — On a unit circle the angle in radians equals the arc length.
- Quadrant I (0 to π/2) (चतुर्थांश I (0 से π/2)) — All six functions are positive.
- Quadrant II (π/2 to π) (चतुर्थांश II (π/2 से π)) — Only sin and cosec are positive.
- Quadrant III (π to 3π/2) (चतुर्थांश III (π से 3π/2)) — Only tan and cot are positive.
- Quadrant IV (3π/2 to 2π) (चतुर्थांश IV (3π/2 से 2π)) — Only cos and sec are positive.
Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 3. Report a mistake