Convert each of the following as indicated.

Question

a) Convert from polar to rectangular coordinates:

(4,𝜋/3)

b) Convert from rectangular to polar coordinates:

4−4𝑖

Hello! Please help me solve these two problems. I am confused!

Answer 1

pi/3 = 60 degrees

r=4 the hypotenuse of a right triangle with angles 30-60-90 degrees

y = the opposite side = sqr3/2 times 4= 2sqr3

x = adjacent side = 1/2 times 4 = 2

(4, pi/3) = (x,y) = (2, 2sqr3) 2^2 + (2sqr3)(^2 = 4 + 12 = 4^2

4-4i is (4,-4) in rectangular coordinates, where i is measured on the y axis

in polar coordinates the angle is 7pi/8 and r= sqr(4^2 +4^2) = sqr32= 4sqr2

(4sqr2, 7pi/8)