def. an angle is the amount of rotation of a ray about its endpoint
DESCRIPTION
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 . terminal side. vertex. initial side. - PowerPoint PPT PresentationTRANSCRIPT
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