Intro to radians and unit circle F-TF.1 F-TF.2 ANGLES AND ANGLE MEASURE
Dec 13, 2015
An angle on the coordinate plane is in STANDARD POSITION if the vertex is at the origin and one ray is on the positive x-axis.
The ray on the x-axis is called the initial side
The ray that rotates about the center is called the terminal side
ANGLES IN STANDARD POSITION
MEASURING ANGLES
You Try: Draw a 150* angleDraw a -45* angle
If the measure of a an angle is positive, the terminal side is rotated counterclockwise
If the measure of an angle is negative, the terminal side is rotated clockwise
A radian is the measure of an angle in standard position with a terminal side that intercepts an arc with the same length as the radius of the circle.
The circumference of a circle is One complete revolution around a circle equals radians.
Since =360*, then =180.
RADIAN – CLICK FOR ANIMATION
45-45-90 RIGHT TRIANGLE
1
1
45
45
Since this is an isosceles triangle, 2 sides are the same. We will let these congruent sides be 1 and 1.
We can then use the Pythagorean Thm. To find the length of the hypotenuse.
a2+b2=c2
12+12 = c2
2=c2
=c
30-60-90 RIGHT TRIANGLE
60 60
602 2
21 1
3030
Start with an Equilateral Triangle
30
60
2
1Then use Pyth. Thm
a
a2+12=22
a2=3a=