Basic Technical Mathematics, 11th Edition

8.1 Signs of the Trigonometric Functions

• Signs of the Trigonometric Functions in Each of the Four Quadrants • Evaluating Functions Knowing Point on Terminal Side

Recall the definitions of the trigonometric functions that were given in Section 4.2. Here, the point (x, y) is a point on the terminal side of angle $\theta \hspace{0.17em},\hspace{0.17em}$ and r is the radius vector. See Fig. 8.1.

Fig. 8.1

$$\begin{array}{rc}\sin \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{y}{r}}& \csc \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{r}{y}}\\ \cos \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{x}{r}}& \sec \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{r}{x}}\\ \tan \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{y}{x}}& \cot \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{x}{y}}\end{array}$$ (8.1)

As noted before, these definitions are valid for a standard-position angle of any size. In this section, we determine the sign of the trigonometric functions in each of the four quadrants.

We can find the values ...