Polar Coordinates Converting to Rectangular Form

1
Polar Coordinates- Converting to Rectangular Form

• 9.3

2
Converting Polar to Rectangular

• Given polar coordinates (r, ?)
• Change to rectangular
• By trigonometry
• x r cos ?y r sin ?
• Try ( ___, ___ )

r
y
?
x
3
Converting Rectangular to Polar

• Given a point (x, y)
• Convert to (r, ?)
• By Pythagorean theorem r2 x2 y2
• By trigonometry
• Try this one for (2, 1)
• r ______
• ? ______

r
y
?
x
4
Write Polar Equation in Rectangular Form

• Given r 2 sin ?
• Write as rectangular equation

5
Write Polar Equation in Rectangular Form

• Given r 2 sin ?
• We know r2x2y2 and yr sin ?
• Thus multiply both sides by r
• And r22r sin ? and x2y2 2y
• So, x2y2-2y0

6
Write Rectangular Equation in Polar Form

• Consider 2x 3y 6
• As before, usedefinitions