Analytic Trigonometry Barnett Ziegler Bylean. CHAPTER 7 Polar coordinates and complex numbers.

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Presentation transcript:

Analytic Trigonometry Barnett Ziegler Bylean

CHAPTER 7 Polar coordinates and complex numbers

CH 7 - SECTION 1 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)

Converting rectangular to polar

Converting equations Uses the same replacements Ex : change to polar form 3x 2 + 5y = 4 – 3y 2 3r 2 cos 2 ( ө) + 5r sin(ө) = 4 – 3 r 2 sin 2 (ө) 3r 3 = 4 – 5r sin(ө) Ex: change to rectangular form r( 3cos(ө) + 7sin(ө)) = 5

CHAPTER 7 – SEC 3 Complex numbers

Complex plane-Cartesian coordinates

Trig form of complex number Z = x + iy then z = rcos(x) + i rsin(y) In pre - calculus or calculus you will explore the relation between this form of z and the form z = re i ө