SOLUTION: What is the following quotient expressed in polar form: 10*(cos(35 °)+ isin(35 °)) / 5*(cos(100 °) +isin(100 °)) Please enter your answer in cis notation and enter an angle

Algebra ->  Trigonometry-basics -> SOLUTION: What is the following quotient expressed in polar form: 10*(cos(35 °)+ isin(35 °)) / 5*(cos(100 °) +isin(100 °)) Please enter your answer in cis notation and enter an angle      Log On


   



Question 982281: What is the following quotient expressed in polar form:
10*(cos(35 °)+ isin(35 °)) / 5*(cos(100 °) +isin(100 °))
Please enter your answer in cis notation and enter an angle between 0° and 360°.
Thank you in advanced.

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!

10*(cos(35°)+ i*sin(35°))/(5*(cos(100°) + i*sin(100°))) =   (a quotient has the modulus equal to the ratio of modulus and the argument equal to the difference of the arguments)

= 10%2F5.(cos(35°-100°)+ i*sin(35°-100°) = 2*(cos(-65°) + i*sin(-65°)) =   (now replace the angle  -65°  by the angle between  0°  and  360°,  which is  360° - 65° = 295°)

= 2*(cos(295°) + i*sin(295°)).