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

1 Answer
Alan P.
Jan 9, 2017

#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#

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