Introduction to Trig UnitIntroduction to Trig Unit

• Unit Circle

• And Radians

Diagrams page 448 AFM bookDiagrams page 448 AFM book

Unit CircleUnit Circle

• unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane

Other descriptions of radiansOther descriptions of radians

• Radian - Wikipedia, the free encyclopedia

• Radian -- from Wolfram MathWorld

Definition for RadianDefinition for Radian

• You need to know for precalculus

• Is a central angle whose intercepted arc has length the radius of the circle

Definition of PiDefinition of Pi

• Need to know for precalculus

• Is the circumference of a circle divided by its diameter.

RadiansRadians• On the unit circle, the angles are given in

degrees. Another way to measure an angle is with radians. It is like Fahrenheit and Celsius to measure temperature.

2π radians = 360° one complete rotation around the circle

1π radians = 180° a half a rotation

π/2 radians = 90° a fourth of a rotation

Convert from Degree to Radians

• From degrees to radians

• Multiply by •

• Reduce the fraction 180

Example:Convert 90° to radians

90180

90

180

2

Convert Radians to Degrees

From Radians to Degrees

Multiply by

And Reduce the fraction

180

Example Convert 3π/2 to decimal

3 180

2

540

2

270

These techniquesThese techniques

• Are very important and will be used throughout our study of trigonometry.

• So practice will make perfect!

Here is where we are goingHere is where we are going