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
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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.
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Acute angle - less than 90o
Obtuse angle - more than 90o
Right angle - 90o
Straight angle -180o
ANGLES
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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.
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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.
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AC
complementary angles
their measures sum to 180
their measures sum to 90
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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
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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
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How many radians can be "cut off" around a circle of radius r?
θr
r
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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
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x
y
Coterminal angles
65
425
-295
angles that when placed in standard position have the same initial and terminal sides
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x
y