Reciprocal and inverse trigonometric functionsEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

Define \sec\theta, cosec\,\theta and \cot\theta.
State the identity linking \sec and \tan.
State the identity linking cosec and \cot.
Range of y=\sec x?
Where is cosec\,x undefined?
Domain and range of \arcsin x?
Domain and range of \arccos x?
Domain and range of \arctan x?
What are the asymptotes of y=\arctan x?
How is the graph of \arcsin x related to that of \sin x?
Exact value of \arcsin\left(\sin\frac{5\pi}{6}\right)?
Exact value of \arccos\left(-\frac12\right)?
How do you solve cosec\frac{\theta}{2}=2 for 0\le\theta<360^\circ?

Exam questions on Reciprocal and inverse trigonometric functions

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
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
In this question $0\le\theta<360^\circ$ .
Solve $\mathrm{cosec}\frac{\theta}{2}=2$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).