Trigonometry - Symmetry of Trigonometric Functions

IB AA SL: core and optional content

Core: sin A, cos(90°−B) and tan(180°+A). Optional: cosec B.

Given that \(\tan A = \frac{5}{12}\) where \(0{}^\circ < A < 90{}^\circ\) and \(\cos B = -\frac{3}{5}\) where \(180{}^\circ < B < 270{}^\circ\).

Evaluate without using calculators

1. \(\sin A\),
2. \(\mathrm{cosec} B\),
3. \(\cos(90{}^\circ - B)\),
4. \(\tan(180{}^\circ + A)\).