Helen's Blog

11-1

Formulas:

Convert to Rectangular:
x=r cos (theta )
y=r sin (theta)

Convert to Polar:
r=sq. root x^2+y^2
tan(theta)=y/x

Examples:

1) Give the polar point for (3,4)

r= sq. root 3^2 +4^2
= sq. root 9+16
= sq. root 25
=5

tan theta= 4/3
theta= tan inverse (4/3)
=53.130 degrees


Answer : (5, 53.130)
(-5, 233.130)

2) Give the rectangular coordinates for the point (3,30 degrees)

x= 3 cos 30
= 3 ( sq. root 3 /2)
= 3 sq.root 3/2

y= 3 sin 30
= 3 (1/2)
= 3/2

Answer: ( 3 sq.root 3/2, 3/2)