# Analytic Trigonometry - PowerPoint PPT Presentation

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Analytic Trigonometry. Barnett Ziegler Bylean. Polar coordinates and complex numbers. Chapter 7. Polar coordinates. Ch 7 - section 1. Converting a point polar to rectangular. Given (3, 30⁰) From unit circle we know that cos ( ө )= x/r

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Analytic Trigonometry

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## Analytic Trigonometry

Barnett Ziegler Bylean

Polar coordinates and complex numbers

### Chapter 7

Polar coordinates

### Converting a point polar to rectangular

• Given (3, 30⁰)

• From unit circle we know that cos(ө)= x/r

• sin(ө) = y/r

• Thus x = 3cos(30⁰) y = 3 sin(30⁰)

### Examples: convert to rectangular coordinates (cartesian)

• (-3, ) (2, 53⁰)

### Converting rectangular to polar

• Given (,-1) convert to polar coordinate

• r2 = 2 + (-1)2 = 3 + 1 = 4

• r = ± 2

• tan(ө) = ө =

• Thus (2,) or (-2, )

### Converting equations

• Uses the same replacements

• Ex : change to polar form

3x2 + 5y = 4 – 3y2

3r2cos2(ө) + 5r sin(ө) = 4 – 3 r2sin2(ө)

3r3 = 4 – 5r sin(ө)

• Ex: change to rectangular form

• r( 3cos(ө) + 7sin(ө)) = 5

Complex numbers

### Trig form of complex number

• Z = x + iy then z = rcos(x) + irsin(y)

• In pre - calculus or calculus you will explore the relation between this form of z and the form z = reiө