# Trig Graphs

## Keywords

Period:- A periodic function is one which repeats its pattern regularly. The period is the horizontal span covered in one full oscillation (or one full pattern before repeating).
Range:- The interval of values which the function maps into.

## Sine (Sin)

Period: $$360^o$$ or $$2\pi\hspace{4pt}\text{rads}$$
Range: $$-1\leq\sin(\theta)\leq1$$
Note that the $$\sin(0)=0$$, keeping some key points like this in mind will help with sketching.

## Cosine (Cos)

Period: $$360^o$$ or $$2\pi\hspace{4pt}\text{rads}$$
Range: $$-1\leq\sin(\theta)\leq1$$
Note that the $$\cos(0)=1$$. Cos and Sin have the same shape graph, but Cos is transposed (shifted) $$90^o$$ or $$\frac{\pi}{2}\hspace{4pt}\text{rads}$$ to the left.

## Tangent (Tan)

Period: $$180^o$$ or $$\pi\hspace{4pt}\text{rads}$$
Range: $$-\infty < \tan(\theta) < \infty$$
Note that $$\tan(0)=0$$. Also there are vertical asymptotes at $$(90+180n)$$ degrees or $$(\frac{\pi}{2}+n\pi)$$ radians, where $$n$$ is any integer.