Polar Coordinates | Graphing Polar Coordinates | Complex Numbers | Relating Rectangular and Polar |
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x= rcosΘ y=rsinΘ
What formulas do you use to convert polar to rectangular
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(r,Θ)
What does each coordinate mean?
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graph
Plot (-2+4i)
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(1,π)
Convert rectangular to polar: (1,0)
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(0,3)
Convert (3,π/2) to rectangular coordinates
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graph
Plot (3,5π/3)
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z=2(cos45+isin45)
Given z=(√3-i) write the expression in polar form
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3√3/2+3i/2
change polar to rectangular: 3(cos30+isin30)
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(2√ 3,11π/6)
Given Z=3-√3i Write the expression in polar coordinates
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4 petals
Use a graphing utility to graph the polar equation: r=2sinΘ. How many petals does it have?
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2(cos120+isin120)
Given z=(-1+√3i) write the expression in polar form
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(4,7π/6)
change rectangular to polar: (-2√3,-2)
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(-1/2,√3/2)
Convert (-1, -π/3) to rectangular
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(-2,4π/3)
Find another coordinate for the point (2,π/3) where the r<0 and 0<Θ<2π
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Rectangular: -6√3+6i Polar:12(cos150+isin150)
Multiply z=3(cos100+isin100) r=4(cos50+isin50) write answer in both rectangular and polar
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y=-x
change from polar to rectangular and graph: Θ=-π/4
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graph
Transform polar to rectangular and then graph the rectangular equation. r=6sinΘ
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5 Petals
how many petals does the graph 3cos(5Θ) have?
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Rectangular: 3/8 +i(3√3/8) Polar:3/4(cos60+isin60)
Divide z=3(cos100+isin100) r=4(cos40+isin40) write answer in both rectangular and polar
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rectangular: (-4,4π/3) Polar: (2,2√3)
Find another coordinate for the point (-2,4π/3) where the r<0 and 0≤Θ<2π
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