y = cot x on (0, π) and y = cot⁻¹x(0, π) पर y = cot x और y = cot⁻¹x(0, π) par y = cot x aur y = cot⁻¹x
NCERT Fig 2.6 · Class 12 Maths · Chapter 2 · interactive diagram
Parts and what they mean
- y = \cot x on (0, \pi) ((0, \pi) पर y = \cot x) — cot is not defined at 0 and \pi; on (0, \pi) it falls from +\infty to -\infty: one-one and onto \mathbb{R}.
- y = \cot^{-1} x (principal branch) (y = \cot^{-1} x (मुख्य शाखा)) — Domain \mathbb{R}, range (0, \pi): its value is always between 0 and π (never negative!).
- Asymptote x = \pi (अनंतस्पर्शी x = \pi) — cot x goes to -\infty as x comes near π (the y-axis x = 0 is the other asymptote).
- Asymptote y = \pi (अनंतस्पर्शी y = \pi) — \cot^{-1}x comes close to π for large negative x, and close to 0 (the x-axis) for large positive 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.
- Example 2 as a mirror pair (उदाहरण 2 एक प्रतिबिंब युग्म के रूप में) — (a, b) on cot ↔ (b, a) on \cot^{-1}.
- (2\pi/3, -1/\sqrt3) on y = \cot x (y = \cot x पर (2\pi/3, -1/\sqrt3)) — Because \cot\frac{2\pi}{3} = -\frac{1}{\sqrt3}.
- (-1/\sqrt3, 2\pi/3) on y = \cot^{-1}x (y = \cot^{-1}x पर (-1/\sqrt3, 2\pi/3)) — So \cot^{-1}(-\frac{1}{\sqrt3}) = \frac{2\pi}{3} — Example 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 2.6. Report a mistake