Graph of y = sin⁻¹(sin x): a zigzagy = sin⁻¹(sin x) का ग्राफ़: टेढ़ी-मेढ़ी रेखाy = sin⁻¹(sin x) ka graph: zigzag

NCERT Section 2.3 · Class 12 Maths · Chapter 2 · interactive diagram

Parts and what they mean

• y = x for -\frac{\pi}{2} \le x \le \frac{\pi}{2} (-\frac{\pi}{2} \le x \le \frac{\pi}{2} के लिए y = x) — Only here \sin^{-1}(\sin x) = x (the NCERT property).
• y = \pi - x for \frac{\pi}{2} \le x \le \frac{3\pi}{2} (\frac{\pi}{2} \le x \le \frac{3\pi}{2} के लिए y = \pi - x) — Because \sin x = \sin(\pi - x) and \pi - x lies in [-\frac{\pi}{2}, \frac{\pi}{2}].
• Example 6 on the graph (ग्राफ़ पर उदाहरण 6) — At x = \frac{3\pi}{5} the graph is at \pi - \frac{3\pi}{5} = \frac{2\pi}{5}.
• The pattern repeats (पैटर्न दोहराता है) — Its values always stay between -\frac{\pi}{2} and \frac{\pi}{2}; the shape repeats every 2\pi.
• Line y = x (dashed) (रेखा y = x (डैश)) — The zigzag leaves this line outside [-\frac{\pi}{2}, \frac{\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 Section 2.3. Report a mistake