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