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.
