An exact ratio and a rationalised expression
8 written marks
The angle \(\theta\) satisfies \(\displaystyle \tan\theta=-\frac{\sqrt5}{2}\) and \(\displaystyle \frac\pi2\lt \theta\lt \pi\).
Part a · 3 marks
Find \(\sin\theta\) and \(\cos\theta\) exactly.
Part b · 2 marks
Hence evaluate \(\displaystyle \frac{1+\sin\theta}{\cos\theta}\) exactly.
Part c · 3 marks
Let \(\phi=2\pi-\theta\). State the quadrant of \(\phi\), then express \(\cos^{-1}(\cos\phi)\) and \(\sin^{-1}(\sin\theta)\) in terms of \(\theta\).
Complete-answer checking, worked solutions and indicative written criteria.
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