The polar coordinates of a point are given. Find the rectangular coordinates of each point.

Question

The polar coordinates of a point are given. Find the rectangular coordinates of each point.

Part I: 

Write your answer in the form (x,y). 

Part II: 

Write your answer in the form (x,y).  

Answer 1

y = r sinθ

x = r cosθ

Try using this formula to help you solve these problems. To get you started for Part 1 in this equation, r = 12 and θ = 7π/4. Hopefully, this helps!! If you're still struggling, let me know!! I'm happy to schedule a session with you!

Answer 2

(12, 7pi/4) = (12, 315 degrees) or (12, -45 degrees) = (12, -pi/4)

x^2 + y^2 = 144

2x^2 = 144

x^2 = 72

x = sqr72 = 6sqr2

y =-x= -sqr72 = -6sqr2

(x,y) = (6sqr2, -6sqr2) = about (8.484, -8.484)

polar (-2, 7pi/3) = (-2,pi/3)= (-2, 60 degrees) = (2, 240 degrees) in quadrant III

reference angle = 60 degrees

sqr(1+3) = sqr4= 2 = magnitude = hypotenuse of the reference angle

sides are 1 and sqr3

(x,y) = (-1, -sqr3)= about (-1, -1.732)

Answer 3