The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Exact values, quadrants and principal inverse values
Use reference angles and quadrant signs for exact ratios.
Interpret negative angles and angles beyond one revolution.
Distinguish principal inverse values from a complete solution set.
Use the quadrant to choose signs. A unit-circle point is \((\cos x,\sin x)\). Principal ranges: \(\sin^{-1}\) uses \(\displaystyle [- \frac{\pi }{2}, \frac{\pi }{2}]\), \(\cos^{-1}\) uses \([0,\pi]\), and \(\tan^{-1}\) uses \(\displaystyle (- \frac{\pi }{2}, \frac{\pi }{2})\). Inverse notation does not mean reciprocal.