April 17, 2012
9.6 Polar Coordinates - Day 1
Plotting Points
April 17, 2012
Multiple representations of the same
point in polar coordinates.
April 17, 2012
Converting between Polar and
Rectangular Coordinates
Polar and rectangular coordinates
are related in the triangle above as:
tan θ = y/x
sin θ = y/r
cos θ = x/r
Use the following relationships to convert from
rectangular coordinates to polar coordinates:
x = r cos θ
y = r sin θ
Use the following relationships to convert from
polar coordinates to rectangular coordinates:
tan θ = y / x
r 2 = x2 + y2
Plot the point (5, 120º) and convert to rectangular
coordinates.
Plot the point (-1/2, √3/2) and convert to polar
coordinates.
April 17, 2012
More practice with converting between polar and rectangular coordinates.
Use the following relationships to convert from
rectangular coordinates to polar coordinates:
x = r cos θ
y = r sin θ
Use the following relationships to convert from
polar coordinates to rectangular coordinates:
tan θ = y / x
r 2 = x2 + y2
Convert to rectangular coordinates.
Convert to polar coordinates.
1.
1.
(-1, 1)
2.
2.
(0, 2)
April 17, 2012
Polar Coordinates - Day 2
Equation Conversion
Converting an equation from Rectangular to Polar is
pretty simple. Just make the substitution:
x = r cos θ and y = r sin θ
Convert the equations:
1. y = x
2.
4x + 7y - 2 = 0
3.
2xy = 1
4.
x2 + y2 - 8y = 0
April 17, 2012
Converting an equation from Polar to Rectangular
coordinates can be challenging.
Use the relationships to assist you in converting the equations below.
x = r cos θ
y = r sin θ
tan θ = y / x
r2 = x2 + y2
Graph the equations below and find the rectangular equation.
1. r = 2
2. θ = π/3
April 17, 2012
3. r = sec θ
4. r2 = sin 2θ
5. r = 2 / (1 + sin θ)
April 17, 2012