Basic Technical Mathematics, 11th Edition

Chapter 4

1. 1. $\begin{array}{rcl}\hspace{0.17em}-\hspace{0.17em}165\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}360\hspace{0.17em}°\hspace{0.17em}& \hspace{0.17em}=\hspace{0.17em}& 195\hspace{0.17em}°\hspace{0.17em}\\ \hspace{0.17em}-\hspace{0.17em}165\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}360\hspace{0.17em}°\hspace{0.17em}& \hspace{0.17em}=\hspace{0.17em}& \hspace{0.17em}-\hspace{0.17em}525\hspace{0.17em}°\hspace{0.17em}\end{array}$

2. 2. $\begin{array}{l}39^{\hspace{0.17em}\prime \hspace{0.17em}}\hspace{0.17em}=\hspace{0.17em}\left({\displaystyle \frac{39}{60}}\right)\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}0.65\hspace{0.17em}°\hspace{0.17em}\\ 37\hspace{0.17em}°\hspace{0.17em}39^{\hspace{0.17em}\prime \hspace{0.17em}}\hspace{0.17em}=\hspace{0.17em}37.65\hspace{0.17em}°\hspace{0.17em}\end{array}$

3. 3. $\tan 73.8\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}3.44$

   

4. 4. $\cos \theta \hspace{0.17em}=\hspace{0.17em}0.3726\hspace{0.17em};\hspace{0.17em}\theta \hspace{0.17em}=\hspace{0.17em}68.12\hspace{0.17em}°\hspace{0.17em}$

   

5. 5. $\begin{array}{rcl}\text{Let }x& \hspace{0.17em}=\hspace{0.17em}& \text{distance from course to east}\\ {\displaystyle \frac{x}{22.62}}& \hspace{0.17em}=\hspace{0.17em}& \sin 4.05\hspace{0.17em}°\hspace{0.17em}\\ x& \hspace{0.17em}=\hspace{0.17em}& 22.62\sin 4.05\hspace{0.17em}°\hspace{0.17em}\\ \hspace{0.17em}=\hspace{0.17em}& 1.598\text{ km}\end{array}$

   

6. 6. $\begin{array}{l}\sin \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{2}{3}}\\ x\hspace{0.17em}=\hspace{0.17em}\sqrt{3^2\hspace{0.17em}-\hspace{0.17em}{2}^2}\hspace{0.17em}=\hspace{0.17em}\sqrt{5}\\ \tan \theta \hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{2}{\sqrt{5}}}\end{array}$

   

7. 7. $\tan \theta \hspace{0.17em}=\hspace{0.17em}1.294\hspace{0.17em};\hspace{0.17em}\csc \theta \hspace{0.17em}=\hspace{0.17em}1.264$

8. 8.