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
- Identifying Sides of Right Triangles
- Right Triangle Trigonometry: Intro
- Trigonometric Ratios (Right Triangle Context)
- What "CO" in COsine Means
- Trigonometric Functions of Special Angles
- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Application Problems
- 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]
Identifying Sides of Right Triangles
The applet below provides an introduction as to how we label the legs of a right triangle with respect to ONE of its acute angles. (Notice angle A, B, A', and B' are acute angles of a right triangle.) [br][br]The triangles shown below are similar triangles. Can you explain why?
1) How would you describe the hypotenuse of a right triangle? What is it? How do you easily find it? [br][br]2) How, within a right triangle, would you be able to identify an acute angle's OPPOSITE LEG? [br][br]3) How, within a right triangle, would you be able to identify an acute angle's ADJACENT LEG?
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.
How Fast are You Spinning?
Our Earth is ALWAYS spinning. Yet, j[i]ust how fast[/i] is earth rotating? [br][br]Everyone on Earth spins 360 degrees in a 24 hour period. 360 degrees / 24 hrs = 15 degrees per hour. [br]This is Earth's ANGULAR SPEED ([i]amount of rotation[/i] per [i]unit time[/i]). This remains constant. [br][br]Yet what's [b]NOT CONSTANT[/b] is one's [b]LINEAR SPEED[/b] ([i]distance traveled[/i] per [i]unit time[/i]). [br]In a 24 hour period, we all--(unless we're flying a great distance in an airplane)--"spin along" a circle of latitude. [br]Some circles of latitude are bigger than others. (Observe in the applet below.) [br]Since this is the case, we [b]CANNOT ALL HAVE the same LINEAR SPEED[/b] as every other person on the planet! [br][br][color=#1551b5][b]Let's assume Earth to be a perfect sphere [/b][/color]([i]for simplicity's sake![/i]) [br]According to NASA's website (http://solarsystem.nasa.gov/planets/profile.cfm?Display=Facts&Object=Earth), [br]Earth has a [color=#d69210][b]mean radius of 3,958.8 miles.[/b][/color] [br]To successfully answer the 2 questions in this applet, all you will need is the following: [br][br]1) [color=#b20ea8]The latitude of your location [/color][br]2) A good working knowledge of some basic geometry formulas. [br]3) A good working knowledge of basic right-triangle trigonometry. [br][br]Have fun with this! [b]([i]Don't check a checkbox before answering the question that precedes it![/i])[/b]