Harmonic form and trigonometric proofEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

Harmonic form of a\cos\theta+b\sin\theta?
What is R called?
\tan\alpha in R\cos(\theta-\alpha)?
Maximum and minimum of R\sin(\theta+\alpha)?
When does a\cos\theta+b\sin\theta=c have no solution?
Expand R\sin(\theta-\alpha).
Express 3\cos\theta+4\sin\theta as R\cos(\theta-\alpha).
Express \sin\theta-\cos\theta as R\sin(\theta-\alpha).
How do you prove an identity?
Why not work on both sides of an identity at once?
1+\cos2\theta and 1-\cos2\theta in simple form?
Prove: \cos x\cos2x+\sin x\sin2x equals?
Why factorise rather than divide by \tan\theta?

Exam questions on Harmonic form and trigonometric proof

Let $h(\theta)=7\cos\theta-24\sin\theta$ , where $\theta$ is measured in degrees.
Find the maximum value of $h(\theta)$ and the smallest positive value of $\theta$ at which it occurs, giving $\theta$ to 1 decimal place.2 marks
Consider the expression $E=\cos x\cos2x+\sin x\sin2x$ .
Prove that $E\equiv\cos x$ , and hence solve $E=\frac12$ for $0\le x<360^\circ$ .2 marks
Consider the identity $\dfrac{\sin2\theta}{1+\cos2\theta}\equiv\tan\theta$ .
Prove that the identity is true.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).