Reflection: Connection to Prior Knowledge What do Triangles have to do with Circles? - Section 3: Transition to the Unit Circle

 

Trigonometry is one of those topics that simply baffles many people.  Strange names for even stranger relationships and an unending list of formulas to memorize make it difficult even for good students.  So, how can we make trigonometry easier to comprehend?

By making it grow out of geometry!

This only works, however, if geometry is something familiar and comprehensible.  In this case, I'm relying on my students' intimate knowledge of the geometry of circles.  They should have learned in a previous course that all circles are similar to one another (G-C1).  Not only that, but when they hear the statement "all circles are similar", they should immediately associate it with notions of ratios and proportions.  If they do, then it will help them understand sine and cosine.  After all, sine and cosine are defined both as ratios!

On the other hand, if your students are not sufficiently familiar with these concepts from geometry, then you'll need to spend a little time reminding them.  The Weekly Workout is a great tool for this!  I'll make a point of including some geometry problems having to do with similar triangles and circles in the weeks leading up to this lesson.  This review is well worth the time; not only will your students benefit from a deeper knowledge of geometry, but they will have a chance at understanding trigonometry in a way that few others do.

  Growing Trig out of Geometry
  Connection to Prior Knowledge: Growing Trig out of Geometry
Loading resource...
 

What do Triangles have to do with Circles?

Unit 9: Trigonometric Functions
Lesson 1 of 8

Objective: SWBAT apply knowledge of trigonometric ratios in right triangles to the unit circle. SWBAT use trigonometric ratios and the unit circle to solve problems.

Big Idea: How is the unit circle related to "triangle measurement"? A story of two equivalent definitions.

  Print Lesson
9 teachers like this lesson
Subject(s):
Math, Trigonometric functions, Trigonometry, unit circle, Algebra, master teacher project, sine, cosine
  45 minutes
ptolemy chord resized
 
1
2
3
4
Similar Lessons
 
Riding a Ferris Wheel - Day 2 of 2
12th Grade Math » Trigonometric Functions
Big Idea: Make the transition from the Ferris wheel problem to the unit circle.
  Favorites(3)
  Resources(10)
Troy, MI
Environment: Suburban
Tim  Marley
 
Investigating Radians
12th Grade Math » Rotations and Cyclical Functions
Big Idea: Students use cylinders and string to investigate radian angle measurements and then use their findings to develop a method to convert from radian to degrees.
  Favorites(7)
  Resources(19)
Phoenix, AZ
Environment: Urban
Tiffany Dawdy
 
The Unit Radius and the Unit Hypotenuse
12th Grade Math » Trigonometry: The Unit Circle
Big Idea: The unit circle provides a rich landscape in which students can find surprising patterns as they have the experience of creating real mathematics.
  Favorites(0)
  Resources(16)
Worcester, MA
Environment: Urban
James Dunseith
 
 
Something went wrong. See details for more info
Nothing to upload
details
close