1. Analytic Trigonometry Barnett Ziegler Bylean

2. CHAPTER 7 Polar coordinates and complex numbers

3. CH 7 - SECTION 1 Polar coordinates

5. 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)

6. Examples: convert to rectangular coordinates (cartesian)

7. Converting rectangular to polar

8. 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

9. CHAPTER 7 – SEC 3 Complex numbers

10. Complex plane-Cartesian coordinates

11. 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