IB Maths AA HL AA 3.3 Trigonometric identities and equations questions

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Question 1

Paper 1, no calculatorHard6 marks

A circuit model represents the normalized voltage at phase $\phi$ by $v(\phi)=\sin\phi$ A controller operates at phase $\theta$ where $0<\theta<\frac{\pi}{2}$ During calibration, the normalized voltage at phase $2\theta$ is $\frac12$

(a)

Starting from the compound-angle identities, derive the double-angle identities for $\sin 2x$ $\cos 2x$ and $\tan 2x$

[3]

(b)

Determine all possible exact values of $\tan\theta$

[3]

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