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Precalculus Review Materials

Jane Butterfield, Gary MacGillivray

Section 5.6 Graphs of Trig Functions

The graphs of the six trig functions are shown below. The trig functiosn 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 \(-2\pi\lt x \lt 4\pi\text{.}\)
Figure 5.6.1.
Graph of \(y=\cos(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Figure 5.6.2.
Graph of \(y=\tan(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Figure 5.6.3.
Graph of \(y=\cot(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Figure 5.6.4.
Graph of \(y=\sec(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Figure 5.6.5.
Graph of \(y=\csc(x)\) for \(-2\pi\lt x \lt 4\pi\text{.}\)
Figure 5.6.6.
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