1.
Without using pencil and paper or a calculator, give the supplement of each angle.
- [latex]30°[/latex]
- [latex]45°[/latex]
- [latex]120°[/latex]
- [latex]25°[/latex]
- [latex]165°[/latex]
- [latex]110°[/latex]
Chapter 3: Laws of Sines and Cosines
Practice each skill in the Homework Problems listed.
Suggested homework problems
Without using pencil and paper or a calculator, give the supplement of each angle.
Without using pencil and paper or a calculator, give the complement of each angle.
For Problems 3–6,
For Problems 7–10,
For Problems 11–20,
The point [latex]-5, 12[/latex] is on the terminal side.
The point [latex]12, 9[/latex] is on the terminal side.
[latex]\cos \theta = -0.8[/latex]
[latex]\cos \theta = \dfrac{5}{13}[/latex]
[latex]\cos \theta = \dfrac{3}{11}[/latex]
[latex]\cos \theta = \dfrac{-5}{6}[/latex]
[latex]tan \theta = \dfrac{-1}{6}[/latex]
[latex]tan \theta = \dfrac{9}{5}[/latex]
[latex]tan \theta = 4[/latex]
[latex]tan \theta = -1[/latex]
Fill in exact values from memory without using a calculator.
| [latex]\theta[/latex] | [latex]~~~0°~~~[/latex] | [latex]~~~30°~~~[/latex] | [latex]~~~45°~~~[/latex] | [latex]~~~60°~~~[/latex] | [latex]~~~90°~~~[/latex] | [latex]~~~120°~~~[/latex] | [latex]~~~135°~~~[/latex] | [latex]~~~150°~~~[/latex] | [latex]~~~180°~~~[/latex] |
| [latex]\cos \theta[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] |
| [latex]\sin \theta[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] |
| [latex]tan \theta[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] |
Use your calculator to fill in the table. Round values to four decimal places.
| [latex]\theta[/latex] | [latex]~~~15°~~~[/latex] | [latex]~~~25°~~~[/latex] | [latex]~~~65°~~~[/latex] | [latex]~~~75°~~~[/latex] | [latex]~~~105°~~~[/latex] | [latex]~~~115°~~~[/latex] | [latex]~~~155°~~~[/latex] | [latex]~~~165°~~~[/latex] |
| [latex]\cos \theta[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] |
| [latex]\sin \theta[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] |
| [latex]tan \theta[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] | [latex]~[/latex] |
For each angle [latex]\theta[/latex] in the table for Problem 22, the angle [latex]180° - \theta[/latex] is also in the table.
Describe and explain any patterns of equal values you see in the table for Problem 22.