AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.8 The Tangent Function
Notes
$\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}$, the slope of the terminal ray.
- Period $\pi$; vertical asymptotes where $\cos\theta=0$ ($\displaystyle \frac{\pi}{2}+n\pi$).
- Increasing on each interval between asymptotes.
Practice
The period of $y=\tan x$:
It repeats every $\pi$.
$\displaystyle \tan\frac{\pi}{4}=$
$\displaystyle \frac{\sqrt2/2}{\sqrt2/2}$.
$\tan x$ has vertical asymptotes at:
Where cosine is 0.
Ready for more? Take the Unit 3 test.