Polar Coordinates Review

Express the polar coordinates (√2, -3π/4) as Cartesian coordinates.

(-1, -1)

Convert the following polar coordinates to its equivalent Cartesian coordinates. (3,270°)

(0,-3)

Match the following items. 1. r = 5 2. r = 3 + 5cosθ 3. r = 5 + 5cosθ 4. r = cos5θ 5. r = 5cosθ

1. circle, center at pole 2. looped limaçon 3. cardioid 4. rose 5. circle, intercepts pole

Which of the following expressions is equal to the argument of -3 + 2i?

180° - tan^-1 |-2/3|

Complete the statement below. The ninth roots of unity are separated by ____ degrees.

40

Determine in which quadrant the product of 2(cos3π/5 + isin3π/5) and 4(cosπ/4 + isinπ/4) lies.

II

eccentricity

a positive constant that indicates the general shape of a conic section

polar coordinate

an ordered pair ( r, θ) where r is the distance from the pole to a point and θ is the angle measured from the initial side to the terminal side

directrix

fixed line of a conic section

focus

fixed point of a conic section

Graph the points having the polar coordinates (-2, 4π/3) by dragging the dot below and dropping it where the point is located.

https://ibb.co/52wPYmf

Identify the conic whose equation is given. r = 4/2-4cosθ

hyperbola

Convert x² + y² = 8 to a polar equation.

r² = 8

argument

the angle of rotation of a complex number in polar form

modulus

the distance that a complex number is from the pole (origin); the absolute value of a complex number

hyperbola

the locus of points for which the difference of the distances from two fixed points is constant

parabola

the locus of points for which the distances from a line (the directrix) and a fixed point (the focus) are equal

ellipse

the locus of points for which the sum of the distances from two fixed points is constant

Convert the polar equation θ = 60° to a Cartesian equation.

y = √3x