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Analytic Trigonometry

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  1. Analytic Trigonometry Barnett Ziegler Bylean

  2. Polar coordinates and complex numbers Chapter 7

  3. Polar coordinates Ch7 - section 1

  4. 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)

  5. Examples: convert to rectangular coordinates (cartesian) • (-3, ) (2, 53⁰)

  6. 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, )

  7. 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

  8. Complex numbers Chapter 7 – sec 3

  9. Complex plane-Cartesian coordinates

  10. 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