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2022 Mathematics Extension 2 Q11 (a) (iii) | HSC Atlas

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2022TrialShort answer

Q11 (a) (iii)

2 marks

Question

Hence find the exact value of $\tan\frac{5\pi}{12}$ .

Try the question before revealing the answer.

Solution

$\frac{-1+i\sqrt3}{1+i}=\sqrt2\operatorname{cis}\frac{5\pi}{12}$

$\tan\frac{5\pi}{12}=2+\sqrt3$

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Complex Numbers

Geometric representation of a complex numberRepresent complex numbers in the complex plane and use modulus, argument and polar form with their identities.

Source

Girraween 2022 4U Trial PaperGirraweenQuestion paper page 6Guidance page 14View original source ↗

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