$\text{cis}(θ)=\cos θ+i\sin θ$. The expression $\dfrac{(\text{cis}\ 75^\circ)(\text{cis}\ 80^\circ−1)}{\text{cis}\ 8^\circ−1}$ can be written as $r\ \text{cis}\ \theta$ where $0 \le \theta < 360^\circ$. Find $\theta$ in degrees.
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HINT:
cis$(2y)-1=\cos2y+i\sin2y-1=-2\sin^2y+2i\sin y\cos y$
$=2i\sin y(\cos y+i\sin y)=2i\sin y\cdot $cis$(y)$
Here $2y=8^\circ,80^\circ$
We may use : How to prove Euler's formula: $e^{it}=\cos t +i\sin t$?
lab bhattacharjee
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I simplified it down to $\dfrac{\text{cis} \ 75^\circ \sin 40 ^\circ \ \text{cis} \ 40^\circ}{\sin 4^\circ \ \text{cis} \ 4^\circ}$. What should I do now? – Yuna Kun Jan 15 '17 at 22:37
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@YunaKun, cis$(a)\cdot$cis$(b)/$cis$(c)=$cis$(a+b-c)$ – lab bhattacharjee Jan 16 '17 at 02:25
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That was the formula I was forgetting! Thanks! – Yuna Kun Jan 16 '17 at 22:04