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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=