Right Triangle Trigonometry
Contains Right Triangle Trigonometry Applets
Table of Contents
- Units of Angle/Arc Measure (Radians, Degrees)
- 1 Radian: Clear Definition
- Movie: Radians to Revs
- Angles in Standard Position
- 3 Main Trigonometric Ratios
- Right Triangle Generator for Right Triangle Trigonometry
- Right Triangle Trigonometry: Intro
- Right Triangles: Identifying Sides WRT Acute Angles
- Identifying Trig Ratios: Quick Formative Assessment
- Finding Exact Trig Ratios: Quiz Question Generator
- Finding Acute Angles of Right Triangles
- True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
- Trigonometric Ratios (Right Triangle Context)
- What "CO" in COsine Means
- Trig Ratio Estimations (Right Triangle Context)
- Right Triangle Solver: Formative Assessment
- Right Triangle Trig: Solving for Sides
- Right Triangle Trig: Solving for Sides (2)
- Trigonometric Functions of Special Angles
- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Special Right Triangles: Basic Questions
- Application Problems
- YOUR Linear Speed?
- How Fast are You Spinning?
- Regular Polygons: Perimeter & Area
- Older Versions of Newer Materials
- SOH-CAH-TOA's Failure (II)
- The 3 Main Trigonometric Ratios
- True Meanings of the 3 Trigonometric Ratios within a Right Triangle Context
- 30-60-90 Triangle
1 Radian: Clear Definition
[color=#c51414]One unit of ANGLE or ARC MEASURE which you're probably familiar with is that of a "degree." One degree is 1/360th of a full revolution, right? [/color][br][color=#0a971e]Another unit of ANGLE or ARC MEASURE is a "revolution". 1 revolution = 360 degrees, right? [/color][br][br][color=#1551b5]Well, there is ANOTHER unit of ANGLE or ARC MEASURE with which you'll soon become familiar. [/color] [br][color=#1551b5]This new unit of ANGLE or ARC MEASURE is called a [b]RADIAN[/b]. [/color] [br][br][i][color=#b20ea8]Interact with the applet below for a few minutes. [br]Reset it a few times and start the animation again each time.[br]Be sure to change the circle's radius as you go along. [br][br][b][color=#1551b5]After interacting with this applet, answer the question that appears immediately below it.[/color][/b][/color] [/i]
Again, recall that a "degree", a "revolution", and a "radian" are all units of ARC MEASURE (i.e. AMOUNT OF SPIN). [br][br][color=#c51414][b]Complete the following sentence definition:[/b][/color] [br][br][b][color=#1551b5]Definition: 1 RADIAN is defined to be a unit of ARC MEASURE for which.....[/color][/b]
Right Triangle Generator for Right Triangle Trigonometry
Math Teachers and Students:
Here, we have a custom tool (far right) that lets you quickly construct a right triangle by simply plotting 2 points and THEN entering the measure of one of its acute interior angles. [br][br][b]Note: [/b][br]If you select the RightTriangle tool (far right), simply plot 2 points. Then, enter in the measure of any acute angle. (You can also, if you choose, enter [math]\alpha[/math] = name of slider) if you wish to quickly change the size of this acute angle.
Quick (Silent) Demo: How to Use
Trig Function Values (30 Degrees)
Interact with the applet below for a few minutes. Then answer the questions that follow.
LARGE POINTS are MOVEABLE. Be sure to slide the slider (lower right) slowly. As you do, pay careful attention to what you see here.
1.
Just by merely observing the dynamics of this applet, what would the [color=#9900ff][b]sine of 30 degrees [/b][/color]be?
2.
What would the [color=#9900ff][b]cosecant of 30 degrees[/b][/color] be?
3.
Do the values of [color=#9900ff][b]either of these ratios[/b][/color] depend upon [color=#666666][b]the length of the circle's radius[/b][/color]? Explain why or why not.
YOUR Linear Speed?
[b]Students:[/b][br][br]Use this applet to help you complete the [i][color=#0000ff]How Fast Are You Spinning?[/color] [/i]investigation given to you at the beginning of class. [br][br]Some key questions to consider are listed below the applet.
1.
According to NASA's website, what is the Earth's mean equatorial radius?
2.
According to your answer for (1), what would Earth's circumference be?
3.
What would the linear speed of a person who lives on the Equator be? (Round your answer to the nearest 10 miles per hour).
4.
What is YOUR current latitude? (For Southern Hemisphere users, use a negative number. For Northern Hemisphere users, use a positive number.) .
5.
Use your answer for (3) and your result for (4) to determine YOUR LINEAR SPEED in miles/hr. (Round to the nearest 10 miles per hour). For a hint, interact with the applet above.