Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Building the Unit Circle

8,644
views

Published on

Published in: Education

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
8,644
On Slideshare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
118
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. By Michael GeiswhiteITC 525 Computers for Educators 2011 Summer Session I
• 2.  History of Trigonometry History of the Unit Circle Important Triangles SOH CAH TOA Ratios Quadrants The Final Unit Circle Fun Facts Standards Credits
• 3.  Hipparchus of Nicaea is known as the father of trigonometry. He compiled the first trigonometric tables to simplify the study of astronomy more than 2000 years ago. He paved the way for other mathematicians and astronomers using triangle ratios. The term “trigonometry” itself emerged in the 16th century, although it derives from ancient Greek roots: “tri” (three), “gonos” (side), and “metros” (measure).
• 4.  The idea of dividing a circle into 360 equal pieces dates back to the sexagesimal (base 60) counting system of the ancient Sumerians. The appeal of 60 was that it was evenly divisible by so many numbers (2, 3, 4, 5, 6, 10, 12, 15, 20, and 30). Early astronomical calculations wedded the sexagesimal system to circles, and the rest is history.
• 5.  30-60-90 Triangle  45-45-90 Triangle
• 6. Click here for a SOHCAHTOA song. SOH CAH TOA is an acronym someone came up with to help us remember how to find the sine, cosine, and tangent values of an angle. We use this in forming the unit circle by using the 30-60-90 and 45-45-90 triangles and ratios. Click here for SOHCAHTOA practice
• 7. Why was the number 60 used as the base for the degrees in a circle?A. It was Hipparchus’ favorite numberB. It is divisible by a lot of numbersC. It was the year they invented trigonometry
• 8. CORRECT! You have a verypromising future in mathematics. GOOD JOB!
• 9. Sorry, your answer is incorrect. Brush up on the history slides and try again.
• 10.  We’re going to use ratios and the two important triangles to build the unit circle. First, we need to remember the definition of ratios. A ratio is a quotient of two numbers or quantities. Also, since we’re building the UNIT circle, we need to remember that “UNIT” means ONE. So we’re going to make each of the hypotenuses of the important triangles equal to one.
• 11.  For the 30-60-90 triangle, we will need to divide each side by 2 so that they hypotenuse will have a length of 1. Therefore, we’re left with a triangle that looks like this:
• 12.  For the 45-45-90 triangle, we will need to divide each side by the square root of 2. We will then need to rationalize each denominator and we’ll end up with a triangle like this:
• 13. Once we have the triangles with 1 for the hypotenuse, what is the side length opposite of 30°?A.B.C.
• 14. CORRECT! YOUR’RE A TRIG MASTER!!! GREAT JOB!