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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

Analytic Trigonometry

Barnett Ziegler Bylean



Ch 7 section 1

Polar coordinates

Ch7 - section 1


Converting a point polar to rectangular
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)



Converting rectangular to polar
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
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


Chapter 7 sec 3

Complex numbers

Chapter 7 – sec 3



Trig form of complex number
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


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