1.
How many degrees are in each angle?
- [latex]\dfrac{3}{5}[/latex] of one rotation
- [latex]\dfrac{3}{10}[/latex] of one rotation
- [latex]\dfrac{4}{3}[/latex] of one rotation
- [latex]\dfrac{8}{3}[/latex] of one rotation
Chapter 4: Trig Functions
Practice each skill in the Homework Problems listed:
How many degrees are in each angle?
How many degrees are in each angle?
What fraction of a complete rotation is represented by each angle?
What fraction of a complete rotation is represented by each angle?
For Problems 7–12, calculate the degree measure of the unknown angle and sketch the angle in standard position.
For Problems 13–18, find two angles, one positive and one negative, that are coterminal with the given angle.
[latex]40°[/latex]
[latex]160°[/latex]
[latex]215°[/latex]
[latex]250°[/latex]
[latex]305°[/latex]
[latex]340°[/latex]
For Problems 19–24, find a positive angle between [latex]0°[/latex] and [latex]360°[/latex] that is coterminal with the given angle.
[latex]-65°[/latex]
[latex]-140°[/latex]
[latex]-290°[/latex]
[latex]-325°[/latex]
[latex]-405°[/latex]
[latex]-750°[/latex]
For Problems 25–30, find the reference angle. Make a sketch showing the angle, the reference angle, and the reference triangle.
[latex]100°[/latex]
[latex]125°[/latex]
[latex]216°[/latex]
[latex]242°[/latex]
[latex]297°[/latex]
[latex]336°[/latex]
For Problems 31–36, find three angles between [latex]90°[/latex] and [latex]360°[/latex] with the given reference angle, and sketch all four angles on the same grid.
[latex]15°[/latex]
[latex]26°[/latex]
[latex]40°[/latex]
[latex]50°[/latex]
[latex]68°[/latex]
[latex]75°[/latex]
For Problems 37–44, use the values given below to find the trigonometric ratio. Do not use a calculator!
[latex]\cos 23° = 0.9205~~~~~~\sin 46° = 0.7193~~~~~~\tan 78° = 4.7046[/latex]
[latex]\cos 157°[/latex]
[latex]\sin 226°[/latex]
[latex]\sin 314°[/latex]
[latex]\cos 203°[/latex]
[latex]\tan 258°[/latex]
[latex]\tan 282°[/latex]
[latex]\sin (-134°)[/latex]
[latex]\cos (-383°)[/latex]
On the circle in the figure, all angles are shown in standard position. Find the measure in degrees of the angles labeled (a)-(i).
Find the reference angle for each of your answers in Problem 45.
Complete the table with exact values.
| [latex]\theta[/latex] | [latex]30°[/latex] | [latex]45°[/latex] | [latex]60°[/latex] | [latex]120°[/latex] | [latex]135°[/latex] | [latex]150°[/latex] | [latex]210°[/latex] | [latex]225°[/latex] | [latex]240°[/latex] | [latex]300°[/latex] | [latex]315°[/latex] | [latex]330°[/latex] |
| [latex]\cos \theta[/latex] | ||||||||||||
| [latex]\sin \theta[/latex] | ||||||||||||
| [latex]\tan \theta[/latex] |
In which two quadrants is the statement true?
Find all angles between [latex]0°[/latex] and [latex]360°[/latex] for which the statement is true.
For Problems 55–60, find a second angle between [latex]0°[/latex] and [latex]360°[/latex] with the given trigonometric ratio.
[latex]\sin 75°[/latex]
[latex]\cos 32°[/latex]
[latex]\tan 84°[/latex]
[latex]\sin 16°[/latex]
[latex]\cos 47°[/latex]
[latex]\tan 56°[/latex]
For Problems 61–66, find all solutions between [latex]0°[/latex] and [latex]360°{.}[/latex] Round to the nearest degree.
[latex]\tan \theta = 8.1443[/latex]
[latex]\sin \theta = 0.7880[/latex]
[latex]\cos \theta = 0.9205[/latex]
[latex]\tan \theta = -3.4874[/latex]
[latex]\sin \theta = -0.9962[/latex]
[latex]\cos \theta = -0.0349[/latex]
For Problems 67–72, find exact values for all solutions between [latex]0°[/latex] and [latex]360°{.}[/latex]
[latex]\cos \theta = -\cos 24°[/latex]
[latex]\tan \theta = -\tan 9°[/latex]
[latex]\sin \theta =-\sin 66°[/latex]
[latex]\cos \theta = -\cos 78°[/latex]
[latex]\tan \theta = -\tan 31°[/latex]
[latex]\sin \theta = -\sin 42°[/latex]
For Problems 73–78, use similar triangles to find the coordinates of the point on the circle.
For Problems 79–82,
Explain why the definitions of the trigonometric ratios for a third-quadrant angle (between [latex]180°[/latex] and [latex]270°[/latex]) are independent of the point [latex]P[/latex] chosen on the terminal side. Illustrate with a figure.
Explain why the definitions of the trigonometric ratios for a fourth-quadrant angle (between [latex]270°[/latex] and [latex]360°[/latex]) are independent of the point [latex]P[/latex] chosen on the terminal side. Illustrate with a figure.