Branches of sin⁻¹: the dark one is the principal value branchsin⁻¹ की शाखाएँ: गहरी शाखा मुख्य मान शाखा हैsin⁻¹ ki branches: dark wali principal value branch hai

NCERT Fig 2.1 (ii) · Class 12 Maths · Chapter 2 · interactive diagram

Parts and what they mean

• Principal value branch of \sin^{-1} (\sin^{-1} की मुख्य मान शाखा) — The branch with range [-\pi/2, \pi/2]. Whenever no branch is mentioned, \sin^{-1} means this one.
• Other branches (अन्य शाखाएँ) — Ranges like [\pi/2, 3\pi/2] or [-3\pi/2, -\pi/2] also make a valid inverse — but they are not the principal one.
• Lines y = \pm\pi/2 (रेखाएँ y = \pm\pi/2) — The principal branch lives between these two lines (both included).
• End points (\pm 1, \pm\pi/2) (अंत बिंदु (\pm 1, \pm\pi/2)) — \sin^{-1}(1) = \pi/2 and \sin^{-1}(-1) = -\pi/2: closed (filled) ends.
• 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 (ii). Report a mistake