# How do you perform the operation in trigonometric form (5(cos4.3+isin4.3))/(4(cos2.1+isin2.1))?

Jan 9, 2017

$\textcolor{g r e e n}{- 0.736 + i 1.011}$ (approx.)

#### Explanation:

$\textcolor{red}{\text{~~~ Trigonometric Division ~~~~~~~~~~~~~~~~~~~~~~}}$
color(white)("XX ")color(blue)((cos(theta)+i * sin(theta))/(cos(phi)+i * sin(phi)))

color(white)("XXX")color(blue)(= [color(green)((cos(theta) * cos(phi) + sin(theta) * sin(phi))] +i * [color(magenta)(sin(theta) * cos(phi)-cos(theta) * sin(phi))]

$\textcolor{red}{\text{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$

$\frac{5 \left(\cos \left(4.3\right) + i \sin \left(4.3\right)\right)}{4 \left(\cos \left(2.1\right) + i \sin \left(2.1\right)\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{5}{4} \cdot \left(\frac{\cos \left(4.3\right) + i \sin \left(4.3\right)}{\cos \left(2.1\right) + i \sin \left(2.1\right)}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \frac{5}{4} \cdot \left[\left(\cos \left(4.3\right) \cdot \cos \left(2.1\right) + \sin \left(4.3\right) \cdot \sin \left(2.1\right)\right)\right) + i \cdot \left(\left(\sin \left(4.3\right) \cdot \cos \left(2.1\right) - \sin \left(2.1\right) \cdot \cos \left(4.3\right)\right)\right]$

(assuming I can use a calculator correctly)
$\textcolor{w h i t e}{\text{XXX}} = \frac{5}{4} \cdot \left[- 0.5885011173 + i \cdot 0.8084964038\right]$

$\textcolor{w h i t e}{\text{XXX}} = - 0.7356263966 + i \cdot 1.0106205048$