Basic Technical Mathematics, 11th Edition

CHAPTER 8 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

1. If $\theta$ is a fourth-quadrant angle, then $\cos \theta \hspace{0.17em}>\hspace{0.17em}0.$

2. $\sin 40\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\sin 220\hspace{0.17em}°\hspace{0.17em}$

3. For $0\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}<\hspace{0.17em}\theta \hspace{0.17em}<\hspace{0.17em}360\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em},\hspace{0.17em}\sin \theta \hspace{0.17em}>\hspace{0.17em}0\hspace{0.17em},\hspace{0.17em}$ and $\tan \theta \hspace{0.17em}<\hspace{0.17em}0\hspace{0.17em},\hspace{0.17em}$ then $\sec \theta \hspace{0.17em}>\hspace{0.17em}0.$

4. To convert an angle measured in radians to an angle measured in degrees, multiply the number of radians by $180\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}/\hspace{0.17em}\pi \hspace{0.17em}.\hspace{0.17em}$

5. The length of arc s of a circular arc of radius r and central angle $\theta$ (in radians) is $s\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{2}}\theta r\hspace{0.17em}.\hspace{0.17em}$

6. If the sine and cosine of an angle are both negative, then the angle must terminate in the third quadrant.

PRACTICE AND APPLICATIONS

In Exercises 7–10, find the trigonometric functions of $\theta \hspace{0.17em}.\hspace{0.17em}$ The terminal side of $\theta$ passes through the given point. ...