# How do you graph y=cosx+tan(2x)?

Dec 28, 2016

Socratic graph for two periods $2 \pi$ is inserted.

#### Explanation:

The period of cos x is $2 \pi$ and the period of tan (2x) is $\frac{\pi}{2}$.

So, the period of cos x + tan 2x is $2 \pi$.

x = an odd mutiple of $\frac{\pi}{2}$ is an asymptote, in both directions

$\uparrow \mathmr{and} \downarrow$.

The inserted graph is for a double period $x \in \left[- 2 \pi , 2 \pi\right]$

x = 0 is the divider, for this double-period graph.

y-intercept is 0.752, nearly, from cos x + tan (2x) = 0.

graph{cos x + tan (2x) [-6.28, 6.28, -5, 5]}