Reciprocal and inverse trigonometric functionsAQA A-Level Maths: Flashcards

What these 14 flashcards ask

Define \sec\theta.
Define \operatorname{cosec}\theta.
Define \cot\theta.
Identity linking \sec^2\theta and \tan^2\theta?
Identity linking \operatorname{cosec}^2\theta and \cot^2\theta?
Range of y=\sec x?
Range of y=\cot x?
Where is y=\operatorname{cosec}x undefined?
Domain and range of \arcsin x?
Domain and range of \arccos x?
Domain and range of \arctan x?
How is the graph of an inverse trig function related to the original?
Value of \arcsin\left(\sin\frac{5\pi}{6}\right)?
Which identity do you use to turn \sec^2\theta and \tan\theta into a quadratic in \tan\theta?

Exam questions on Reciprocal and inverse trigonometric functions

The angle $\theta$ is acute and $\sin\theta=\frac35$ .
Find the exact value of $\sec\theta+\tan\theta$ .2 marks
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
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

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).