Trigonometry - Exact Trigonometric Values and the Unit Circle

IB AA SL: core and optional content

Core: find sin θ. Optional: find cot θ and cosec θ.

Given that \(\cos \theta = -\frac{2}{5}\) and \(\frac{\pi}{2} < \theta < \pi\), without using a calculator, find,

1. \(\sin \theta\),
2. \(\cot \theta\),
3. \(\textbf{cosec} \theta\),

exactly.