MATH 107 Lecture Notes - Lecture 3: Polar Coordinate System, Pythagorean Theorem, Rasin
14 Oct 2016
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Renaming Polar Coordinates
1. There are four ways to rename a Polar Coordinate [e.g. (r, θ)] a)
(r,θ360)or(r,θ2π)
b) (r,θ+360)or(r,θ+2π) c) (r,θ+180)or(r,θ+π) d) (r,θ180)or(r,θπ)
C. Converting Between Rectangular and Polar Coordinates
1. Converting from Rectangular to Polara) Given a rectangular point : (3, -7)
2 2 (1) Find r, by using the pythagorean theorem, which is √x + y to
2.
get √58
. (2) Next, find θ by using tan (y/x)
. (3) Your new point is (r, θ).
2. Converting from Polar to Rectangulara) Given a polar coordinate : (3,
π/4)
(1) Find x, which is equal to r cos θ (2) Find y, which is equal to r sin θ (3)
Your new point is (x, y).
D. Converting Between Rectangular and Polar Equations
1. Converting from rectangular equations to polar equations: a) Given an
equation: 3y - 7x = 10
-1
(1) Substitute y and x with r sin θ and r cos θ respectively (2)
Youshouldget3(rsinθ)7(rcosθ)=10(3) Distributeandfactoroutr⇒
r(3sinθ7sinθ)=10 (4) Solveforr⇒ r=10/(3sinθ7sinθ)
2. Converting from polar equations to rectangular equations: a) Given an
equation: r = 4 sin θ
(1) Multiply both sides by r ⇒ r 2 = 4 r sin θ2 2 2 2 2
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Document Summary
/4) (1) find x, which is equal to r cos (2) find y, which is equal to r sin (3) Your new point is (x, y): converting between rectangular and polar equations, converting from rectangular equations to polar equations: a) given an equation: 3y 7x = 10. 1 (1) substitute y and x with r sin and r cos respectively (2) 2 2 equation of a circle, which should be: x + (y 2) = 4. The graph of a polar equation is: r = f( ) 2 2 2 2 a) r = a sin 2 or r = a cos 2 : graphing polar equations. Complex numbers a. graphing complex numbers: on a coordinate plane, the horizontal axis represents the real component, and the vertical axis represents the imaginary component, how to find the modulus ( r ) 2 2, ris=to a +b ,whenz=a+bi 3.
