Converting Rectangular to Polar
The rectangular coordinates for this point are (0, -5).
What is (5, 3pi/2)?
The polar form of this point is (2, 7pi/6).
What is (-sqrt3, -1)?
This is the product of [3/2(cos pi/6 = i sin pi/6)][6(cos pi/4 + i sin pi/4)].
What is 9(cos 5pi/12 + i sin 5pi/12)?
When you use De Moivre's Theorem to find [3(cos 150* + i sin 150*)]^4, you get this.
What is -81/2-(81sqrt3/2)i?
These are the square roots of 16(cos 60* + i sin 60*).
What are 4(cos 30* + i sin 30*) and 4(cos 210* + i sin 210*)?
The rectangular coordinates of this point are (4+4i).
What is 4sqrt2(cos pi/4 + i sin pi/4)?
The trigonometric form of this number is 5(cos 135*+ i sin 135*).
What is -5sqrt2/2 + 5 sqrt2/2 i
This is the product of [1/2(cos 115* + i sin 115*)][4/5(cos 300* + i sin 300*)].
What is 2/5(cos 55* + i sin 55*)?
When you use De Moivre's Theorem to find [2(cos pi/2 + i sin pi/2)]^12, you get this.
What is 4096?
These are the cube roots of -4sqrt2(1-i).
What are 2(cos pi/4 + i sin pi/4), 2(cos 11pi/12 + i sin 11pi/12), and 2 (cos 19pi/12 + i sin 19pi/12)?
The rectangular coordinates of this point are -1+sqrt3i.
What is 2(cos 2pi/3 + i sin 2pi/3)?
The polar form of this point is 8(cos 5pi/6 + i sin 5pi/6).
What is -4sqrt3 + 4i?
This is the product of (cos 5* + i sin 5*)(cos 20* + i sin 20*).
What is cos 25* + i sin 25*?
When you use De Moivre's Theorem to find (2+2i)^6, you get this.
What is -512 i ?
These are the cube roots of 1000.
What are 10(cos 0 + i sin 0), 10(cos 2pi/3 + i sin 2pi/3), and 10(cos 4pi/3 + i sin 4pi/3)?
The rectangular form of this point is 5/2(sqrt3-i).
What is 5(cos 11pi/6 + i sin 11pi/6)?
The polar form of this equation is r=10.
What is x^2 + y^2 = 100?
This is the quotient of [5(cos 4.3 + i sin 4.3)]/[4(cos 2.1 + i sin 2.1)].
What is 5/4 (cos 2.2 + i sin 2.2)?
When you use De Moivre's Theorem to find (1-i)^12, you get this.
What is -64?
These are the fourth roots of 625i.
What are
5(cos pi/8 + i sin pi/8),
5(cos 5pi/8 + i sin 5pi/8),
5(cos 9pi/8 + i sin 9pi/8),
and 5(cos 13pi/8 + i sin 13pi/8)?
The rectangular form of this equation is 3x-6y+2=0.
What is r=-2/(3costheta-6sintheta)?
The polar form of this equation is r=2sec(theta).
What is x=2?
This is the quotient of (cos 7pi/4 + i sin 7pi/4)/(cos pi + i sin pi).
What is cos 3pi/4 + i sin 3pi/4?
When you use De Moivre's Theorem to find 4(1-sqrt3 i)^3, you get this.
What is -32?
These are the fourth roots of -4.
What are
sqrt2(cos pi/4 + i sin pi/4)
sqrt2(cos 3pi/4 + i sin 3pi/4)
sqrt2(cos 5pi/4 + i sin 5pi/4)
and sqrt2(cos 7pi/4+ i sin 7pi/4)?