Basic Technical Mathematics, 11th Edition

10.4 Graphs of y = tan x , y = cot x , y = sec x , y = csc x

• Graph of $y\hspace{0.17em}=\hspace{0.17em}\tan x$ • Reciprocal Functions • Asymptotes • Graphs of $y\hspace{0.17em}=\hspace{0.17em}cotx\hspace{0.17em},\hspace{0.17em}y\hspace{0.17em}=\hspace{0.17em}\sec x\hspace{0.17em},\hspace{0.17em}y\hspace{0.17em}=\hspace{0.17em}\csc x$

The graph of $y\hspace{0.17em}=\hspace{0.17em}\tan x$ is displayed in Fig. 10.23. Because from Section 4.3 we know that $\csc x\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}/\hspace{0.17em}\sin x\hspace{0.17em},\hspace{0.17em}\sec x\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}/\hspace{0.17em}\cos x\hspace{0.17em},\hspace{0.17em}$ and $\cot x\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}/\hspace{0.17em}\tan x\hspace{0.17em},\hspace{0.17em}$ we are able to find values of $y\hspace{0.17em}=\hspace{0.17em}\csc x\hspace{0.17em},\hspace{0.17em}y\hspace{0.17em}=\hspace{0.17em}\sec x\hspace{0.17em},\hspace{0.17em}$ and $y\hspace{0.17em}=\hspace{0.17em}\cot x$ and graph these functions, as shown in Figs. 10.24–10.26.

The following reciprocal relationships are the basis for graphing $y\hspace{0.17em}=\hspace{0.17em}\cot x\hspace{0.17em},\hspace{0.17em}y\hspace{0.17em}=\hspace{0.17em}\sec x\hspace{0.17em},\hspace{0.17em}$ and $y\hspace{0.17em}=\hspace{0.17em}\csc x$.

$$\csc x\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{\sin x}}\sec x\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{\cos x}}\cot x\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{\tan x}}$$ (10.2)

Fig. 10.23

Figure 10.23 Full Alternative ...