y = cosec x on [−π/2, π/2] − {0} and y = cosec⁻¹x[−π/2, π/2] − {0} पर y = cosec x और y = cosec⁻¹x[−π/2, π/2] − {0} par y = cosec x aur y = cosec⁻¹x

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

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Parts and what they mean

y = \operatorname{cosec} x on [-\pi/2, \pi/2] - \{0\} ([-\pi/2, \pi/2] - \{0\} पर y = \operatorname{cosec} x) — Two pieces with the y-axis as asymptote. Range \mathbb{R} - (-1, 1).
y = \operatorname{cosec}^{-1} x (principal branch) (y = \operatorname{cosec}^{-1} x (मुख्य शाखा)) — Domain \mathbb{R} - (-1, 1), range [-\pi/2, \pi/2] - \{0\}. The x-axis is its asymptote, so 0 is never a value.
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 cosec ↔ (b, a) on \operatorname{cosec}^{-1}.
(\pi/6, 2) on y = \operatorname{cosec} x (y = \operatorname{cosec} x पर (\pi/6, 2)) — Because \operatorname{cosec}\frac{\pi}{6} = \frac{1}{\sin(\pi/6)} = 2.
(2, \pi/6) on y = \operatorname{cosec}^{-1}x (y = \operatorname{cosec}^{-1}x पर (2, \pi/6)) — So \operatorname{cosec}^{-1}2 = \frac{\pi}{6} (Exercise 2.1, Q3).
End points (filled) (अंत बिंदु (भरे हुए)) — \operatorname{cosec}^{-1}(1) = \pi/2, \operatorname{cosec}^{-1}(-1) = -\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 2.3. Report a mistake