Trig Graphs


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.
sin graph with key points

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.
cos graph with key points

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.
tan graph with key points