Reciprocal and inverse trigonometric functionsEdexcel A-Level Maths: Mind map

Exam questions on Reciprocal and inverse trigonometric functions

1. The angle $\theta$ is acute and $\tan\theta=\frac{5}{12}$.
   Use the identity $\mathrm{cosec}^2\theta=1+\cot^2\theta$ to confirm your value of $\mathrm{cosec}\,\theta$.2 marks
2. The inverse trigonometric functions $\arcsin$, $\arccos$ and $\arctan$ are defined using their principal values, with angles in radians.
   Find the exact value of $\arcsin\left(\sin\frac{5\pi}{6}\right)$, explaining why it is not $\frac{5\pi}{6}$.2 marks
3. In this question $0\le\theta<360^\circ$.
   Solve $\mathrm{cosec}\frac{\theta}{2}=2$.3 marks