Basic Technical Mathematics, 11th Edition

CHAPTER 20 PRACTICE TEST

As a study aid, we have included complete solutions for each Practice Test problem at the end of this book.

1. Prove that $\sec \theta \hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{\tan \theta }{\csc \theta }}\hspace{0.17em}=\hspace{0.17em}\cos \theta \hspace{0.17em}.\hspace{0.17em}$

2. Solve for $x(0\hspace{0.17em}\le \hspace{0.17em}x\hspace{0.17em}<\hspace{0.17em}2\pi )$ analytically, using trigonometric relations where necessary: $\sin 2x\hspace{0.17em}+\hspace{0.17em}\sin x\hspace{0.17em}=\hspace{0.17em}0\hspace{0.17em}.\hspace{0.17em}$

3. Find an algebraic expression for $\cos ({\sin }^{\hspace{0.17em}-\hspace{0.17em}1}x)\hspace{0.17em}.\hspace{0.17em}$

4. The electric current as a function of the time for a particular circuit is given by $i\hspace{0.17em}=\hspace{0.17em}8.00e^{\hspace{0.17em}-\hspace{0.17em}20t}(1.73\cos 10.0t\hspace{0.17em}-\hspace{0.17em}\sin 10.0t)\hspace{0.17em}.\hspace{0.17em}$ Find the time (in s) when the current is first zero.

5. Prove that ${\displaystyle \frac{\tan \alpha \hspace{0.17em}+\hspace{0.17em}\tan \beta }{\tan \alpha \hspace{0.17em}-\hspace{0.17em}\tan \beta }}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{\sin (\alpha \hspace{0.17em}+\hspace{0.17em}\beta )}{\sin (\alpha \hspace{0.17em}-\hspace{0.17em}\beta )}}\hspace{0.17em}.\hspace{0.17em}$

6. Prove that ${\cot }^{2}x\hspace{0.17em}-\hspace{0.17em}{\cos }^{2}x\hspace{0.17em}=\hspace{0.17em}{\cot }^2{x\cos }^{2}x\hspace{0.17em}.\hspace{0.17em}$

7. Find $\cos {\displaystyle \frac{1}{2}}x$ if $\sin x\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{3}{5}}$ and $270\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}<\hspace{0.17em}x\hspace{0.17em}<\hspace{0.17em}360\hspace{0.17em}°\hspace{0.17em}\hspace{0.17em}.\hspace{0.17em}$

8. The intensity of a certain type of polarized light is given by $I$