Chapter 1.1 Angles and The Trigonometric Functions
area of a sector
1/2r2(radian)
-45 degrees=
1/8 rotation clockwise
pi radians=
180 degrees
circumference
2(pi)r
radius
2pi
when the terminal side makes a full revolution, the radian angle measure is...
2pi r
2pi=
360 degrees
complete rotation
360 degrees
a circle has a radius of 6 inches, find the lenth of the arc intercepted by a central angle of 45 degrees. express arc in terms of pi. round your answer to the nearest 2 decimal places.
4.17 inches
practice problems: Convert these degrees to radians... 60 degrees 270 degrees -300 degrees Convert these radians to degrees... pi/4 radians -4pi/3 radians 6 radians
60 degrees= (pi)/3 radians 270 degrees= (3pi)/2 radians -300 degrees= (5pi)/3 radians 45 degrees -240 degrees 343.8 degrees
a 45rpm record has an angular speed of 45 revolutions per minute. find the linear speed where the needle is 1.5 inches from the records center.
90pi/1 min
acute, right, straight, obtuse
<90, 90, 180, >180
α
alpha
central angle
angle whose vertex is at the center of the circle
coterminal angles
angles that have the same initial and terminal sides but possibly different rotations
w
angular speed w=radians/t
β
beta
negative angle
clockwise
what direction does a negative angle open up to?
clokcwise
what direction does a positive angle open up to?
counter clockwise
positive angle
counterclockwise
3/4 a revolution
coutner clockwise through 3/4 quadrants 3pi/2 radians
how are angles measured?
determining amount of rotation from initial side to terminal side
γ
gamma
linear speed
if a point is in motion on a circle of a radius (r) through an angle of radians in time (t) then linear speed is v=s/t
quadrantal angle
terminal side lies on the x or y axis
radian measure of any central angle of a circle...
is the length of the intercepted arc divided by the circles radius
s=
length of the angle
v
linear speed v=s/t
given the terminal side rotation fraction, how can you find the radian amount, degree measure of angle?
multiple by 2 pi, multiply by 360 degrees
how to convert degrees into radians
multiply degrees by (pi radians)/(180 degrees)
how to convert radians to degrees
multiply radians by (180 degrees)/(pi radians)
initial side
one ray that is the "beginning" of the angle
terminal side
one ray that is the "end" of the angle
1/2 revolution
pi radians counter clockwise through 2 quadrants
1/4 revolution
pi/2 radians counter clock through 1 quadrant
r=
radius of a circle
v=
rw
radian equasion
s/r
angle
two rays that have a common end point
s=
v(radians)
linear speed in terms of angular speed
v=rw
Standard position
when an angles vertex is at the origin of the rectangular coordinate, with its initial side on the positive x axis
angular speed
where s is the arc length given by s=r(radians) its angular speed would be w=radians/t
radian measure=
θ symbol the measure of a central angle of a circle that intercepts an arc equal in length to the radius of the circle
