Section 5.6 Graphs of Trig Functions
The graphs of the six trig functions are shown below. The trig functions are all periodic. (A function is periodic with period \(p\) if \(f(x+p)=f(x)\) for all real numbers \(x\text{.}\) Such a function repeats every \(p\) units along the \(x\)-axis.) Sine and cosine have periods of \(2\pi\text{.}\) Tangent, cotangent, secant, and cosecant all have periods of \(\pi\text{.}\)
Graph of \(y=\sin(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Graph of \(y=\cos(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Graph of \(y=\tan(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Graph of \(y=\cot(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Graph of \(y=\sec(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Graph of \(y=\csc(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
