y = cos x on [0, π] and its mirror y = cos⁻¹x[0, π] पर y = cos x और उसका प्रतिबिंब y = cos⁻¹x[0, π] par y = cos x aur uska mirror y = cos⁻¹x
NCERT Fig 2.2 · Class 12 Maths · Chapter 2 · interactive diagram
Parts and what they mean
- y = \cos x, restricted to [0, \pi] (y = \cos x, [0, \pi] तक सीमित) — On [0, \pi] cos falls steadily from 1 to −1: one-one and onto [-1, 1].
- y = \cos^{-1} x (principal branch) (y = \cos^{-1} x (मुख्य शाखा)) — Domain [-1, 1], range [0, \pi]. Its values are never negative.
- Mirror line y = x (दर्पण रेखा y = x) — Fold the paper along this line: the trig graph lands exactly on the inverse graph. A point (a, b) goes to (b, a).
- Full graph (dashed, faint) (पूरा ग्राफ़ (धुँधला, डैश)) — The trig function on its natural domain — it is not one-one there.
- A point and its mirror (एक बिंदु और उसका प्रतिबिंब) — (a, b) on cos ↔ (b, a) on \cos^{-1}.
- (2\pi/3, -\tfrac12) on y = \cos x (y = \cos x पर (2\pi/3, -\tfrac12)) — Because \cos\frac{2\pi}{3} = -\frac12.
- (-\tfrac12, 2\pi/3) on y = \cos^{-1}x (y = \cos^{-1}x पर (-\tfrac12, 2\pi/3)) — So \cos^{-1}(-\frac12) = \frac{2\pi}{3} (Exercise 2.1, Q5).
- End points (filled) (अंत बिंदु (भरे हुए)) — \cos^{-1}(1) = 0 and \cos^{-1}(-1) = \pi.
- x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
- y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
- Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
Original diagram drawn by Simple Learning Hub, based on NCERT Fig 2.2. Report a mistake