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

Exam questions on Reciprocal and inverse trigonometric functions

1. The angle $\theta$ is acute and $\sin\theta=\frac35$.
   Find the exact value of $\sec\theta+\tan\theta$.2 marks
2. The inverse functions arcsin, arccos and arctan are defined by restricting sine, cosine and tangent to intervals on which each is one-to-one, so each takes its principal value.
   Find the exact value of $\arctan\left(-\sqrt3\right)+\arccos\left(\frac{\sqrt3}{2}\right)$.2 marks
3. Consider the equation $2\sec^2\theta=5-\tan\theta$ for $0\le\theta<2\pi$.
   Show that the equation can be written as $2\tan^2\theta+\tan\theta-3=0$.3 marks