Question

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

Answer 1

`color(green)(-0.736 + i 1.011)` (approx.)

Explanation:

`color(red)("~~~ 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))]`

`color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")`

`(5(cos(4.3)+isin(4.3)))/(4(cos(2.1)+isin(2.1)))`

`color(white)("XXX")=5/4 * ((cos(4.3)+isin(4.3))/(cos(2.1)+isin(2.1)))`

`color(white)("XXX")=5/4 * [(cos(4.3) * cos(2.1) +sin(4.3) * sin(2.1)))+ i * ((sin(4.3) * cos(2.1) - sin(2.1) * cos (4.3))]`

(assuming I can use a calculator correctly)
`color(white)("XXX")=5/4 * [-0.5885011173 + i * 0.8084964038]`

`color(white)("XXX")=-0.7356263966 + i * 1.0106205048`