Pc9-1 polar coordinates notes
- 1. Precalculus 9-1 Polar Coordinates The __________________ coordinate system uses the distance from a fixed point (like the ___________________) and the angle from a fixed _______________. • The origin is called the __________________. • The ______________________________ is the horizontal ray from the pole to the right. • A point P is identified by the coordinates ______________. • r is the ______________________ from the pole to the point. • θ is the ________________ from the Graph the angle first, then find the distance along that line. 7π Example 1: Graph P(3, 60°), Q −1.5, , and R(-2, -135°). 8 There are _____________________ representations of (r, θ): (r, θ + ) ( , θ + (2k + 1)π) where k is any integer. Polar Equations A polar equation is in the form: __________________________________________________________________
- 2. Basic graphs: Example 2: Graph (a) r = 3 and 3p (b) θ = 4 Distance Formula for the polar plane If P1(r1, θ1) and P2(r2, θ2) are two points in the polar plane, then P1P2 = Example 3: While mapping out a level site, a land surveyor identifies a landmark that is 700 feet away and 40° to the left, and another one 350 feet away and 35° to the right. What is the distance between the landmarks? HW p. 558 (16 – 26, 32 – 44 even)