SOLUTION: Convert the given Cartesian coordinates to polar coordinates with r > 0, 0 ≤ 𝜃 ≤ 2𝜋. Remember to consider the quadrant in which the given point is located. (6, −4)

Algebra ->  Trigonometry-basics -> SOLUTION: Convert the given Cartesian coordinates to polar coordinates with r > 0, 0 ≤ 𝜃 ≤ 2𝜋. Remember to consider the quadrant in which the given point is located. (6, −4)      Log On


   

Question 1205038: Convert the given Cartesian coordinates to polar coordinates with
r > 0, 0 ≤ 𝜃 ≤ 2𝜋.
Remember to consider the quadrant in which the given point is located.
(6, −4)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Convert the given Cartesian coordinates to polar coordinates with
r+%3E+0, 0+%3C=+theta+%3C=+2pi
(6, 4)

Polar Coordinates (r,theta):
r+=+sqrt%28+x%5E2+%2B+y%5E2+%29+
r+=+sqrt%28+6%5E2+%2B+%28-4%29%5E2+%29+
r+=+sqrt%28+36+%2B+16+%29+
r+=+sqrt%28+52+%29+
r=2sqrt%2813%29

theta+=+tan%5E-1+%28+y+%2F+x+%29
theta+=+tan%5E-1+%28+-4+%2F+6+%29
theta+=+tan%5E-1+%28+-2+%2F+3+%29
theta+=+-33.69°
angle is in quadrant 4
(r,theta)= (2sqrt%2813%29,-33.69°)
or, approximately
(r,theta)= (7.2,-33.69°)