def. an angle is the amount of rotation of a ray about its endpoint

Def. An angle is the amount of rotation of a ray about its endpoint.

Def. An angle formed by rotation a ray 1/360 of a complete rotation has a measure of one degree, denoted by

initial side

term

inal

side

vertex

Note: We can measure an angle using either in degrees or radians.

Acute angle - less than 90o

Obtuse angle - more than 90o

Right angle - 90o

Straight angle -180o

ANGLES

x

y

initial side

terminal side

vertex

standard position for an angleits vertex is at the origin and

its initial side is the positive x-axis

A positive angle has a counterclockwise rotation. A negative angle has

a clockwise rotation.

0 , 360

90

180

270

Def. A quandrantal angle has its terminal side coinciding with one of the axes when it's in standard position.

AC

complementary angles

their measures sum to 180

their measures sum to 90

Def. A central angle is a positive angle whose vertex is the center of a circle and whose initial and terminal sides intercept the circle forming an arc.

θ

Def. If a central angle intercepts an arc equal in length to the radius of the circle, it has a measure of 1 radian.

θr

r r

How many radians can be "cut off" around a circle of radius r?

θr

r

Right Triangle Pythagorean

Theorema

b

c

2 legs are equal and thehypotenuse is 2 times as long as either leg

hypotenuse is 2 times as long as the short leg and long leg is 3 times as long as the short leg

x

y

Coterminal angles

65

425

-295

angles that when placed in standard position have the same initial and terminal sides

x

y