Medium Practice — Set 2

Quick Recap — Inverse Trig & Triangles

• Principal ranges: $\sin^{-1}x\in[-\tfrac{\pi}{2},\tfrac{\pi}{2}]$, $\cos^{-1}x\in[0,\pi]$, $\tan^{-1}x\in(-\tfrac{\pi}{2},\tfrac{\pi}{2})$.
• $\sin^{-1}x+\cos^{-1}x=\tfrac{\pi}{2}$; $\tan^{-1}x+\cot^{-1}x=\tfrac{\pi}{2}$.
• Sine rule: $\tfrac{a}{\sin A}=\tfrac{b}{\sin B}=\tfrac{c}{\sin C}=2R$; cosine rule: $a^2=b^2+c^2-2bc\cos A$.
• Area of a triangle $=\tfrac12ab\sin C$; in any triangle $A+B+C=\pi$.