Trigonometric and Polar Functions

100 meters

25 meters

75 meters

50 meters

$\pi(a b) \times \left( \frac{\text{directrix distance}}{\text{eccentricity} \times \text{focal length}} \right)$

$ab \times \frac{\text{eccentricity}}{\text{focal length}} \times \text{directrix distance}$

$\pi(a b) \times \left( \frac{\text{eccentricity} \times \text{focal length}}{\text{directrix distance}} \right)$

$\frac{\pi(ab)}{\text{eccentricity} \times \text{focal length} \times \text{directrix distance}}$

$r=\tan(\theta+\frac{\pi}{6})$

$r=\tan(\theta-\frac{\pi}{12})$

$r=\tan(\theta-\sqrt{3})$

$r=\tan(\theta-\frac{\pi}{6})$

45°

360°

90°

180°

$r=1+\sin(\frac{\theta}{2})$

$r=0\theta$

$r=1+0\theta$

$r=1+\sin(0\theta)$

A sine or cosine function with a period of one year.

An exponential growth function with a base corresponding to daylight hours.

A linear function increasing throughout one year.

A tangent function with a period of one year.

$\sqrt{2}$

$-1$

$1$

$0$

$\theta = \pi$

$\theta = \frac{\pi}{6}$

$\theta = 0$

$\theta = \frac{\pi}{2}$

$\frac{\pi}{4}$

$2\pi$

$\pi$

$\frac{\pi}{2}$

$\arctan(\sqrt{\frac{27}{16}})-\pi$

$(\arctan(\sqrt{\frac{27}{16}})+\pi)$

$(\arctan(\sqrt{1627})+\frac{\pi}{4})$

$\arctan(\sqrt{\frac{27}{16}})$