AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.13 Trigonometry and Polar Coordinates
Notes
- Polar $(r,\theta)$ to rectangular: $x=r\cos\theta$, $y=r\sin\theta$.
- Rectangular to polar: $r^2=x^2+y^2$, $\displaystyle \tan\theta=\frac{y}{x}$ (check the quadrant).
- Complex numbers: $a+bi=r(\cos\theta+i\sin\theta)$.
Practice
$\displaystyle (4,\frac{\pi}{3})$ in rectangular:
$\displaystyle 4\cdot\frac{1}{2}$, $\displaystyle 4\cdot\frac{\sqrt3}{2}$.
$(0,-3)$ in polar (with $r>0$):
Straight down.
The modulus $r$ of $3+4i$:
$\displaystyle \sqrt{9+16}$.
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