Polar

so since we just reviewed trig stuff I am going to blog on polar points and rectangular points and how to convert both ways.

In polar they use a radius and an angle, (r, Θ), instead of a vertical and horizontal values, (x, y), which is a rectangular point.

to convert from polar to rectangular

• x = r cos Θ


• y = r sin Θ

to convert from rectangular to polar

• r = √x²+y²


• Θ= arctan (y/x)

Example 1: give the polar coordinates for the point (5, 5)

r = √5²+5²

r = √50

r = ±5√2

Θ = arctan (5/5)

Θ = 45°, 255°

(5√2, 45°)

(-5√2, 225°)

Example 2: give the rectangular coordinates for (4, 30°)

x = 4 cos (30°)

x = 4 * (√3)/2

x = 2√2

y = 4 sin (3o°)

y = 4 *(1/2)

y = 2

( 2√2, 2 )