y = sin x on [−π/2, π/2] and its mirror y = sin⁻¹x[−π/2, π/2] पर y = sin x और उसका प्रतिबिंब y = sin⁻¹x[−π/2, π/2] par y = sin x aur uska mirror y = sin⁻¹x
NCERT Fig 2.1 (iii) · Class 12 Maths · Chapter 2 · interactive diagram
Parts and what they mean
- y = \sin x, restricted to [-\pi/2, \pi/2] (y = \sin x, [-\pi/2, \pi/2] तक सीमित) — Here sin is one-one and onto [-1, 1] — so it has an inverse.
- y = \sin^{-1} x (principal branch) (y = \sin^{-1} x (मुख्य शाखा)) — Domain [-1, 1], range [-\pi/2, \pi/2]. It is the blue curve flipped in y = x.
- 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) — The dashed segment is perpendicular to y = x; its middle lies on y = x.
- (\pi/6, \tfrac12) on y = \sin x (y = \sin x पर (\pi/6, \tfrac12)) — Because \sin\frac{\pi}{6} = \frac12.
- (\tfrac12, \pi/6) on y = \sin^{-1}x (y = \sin^{-1}x पर (\tfrac12, \pi/6)) — Swap the coordinates: \sin^{-1}\frac12 = \frac{\pi}{6}.
- End points (filled) (अंत बिंदु (भरे हुए)) — Ends are included: \sin^{-1}(\pm1) = \pm\pi/2.
- 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 2.1 (iii). Report a mistake