Chapter 1.1 Angles and The Trigonometric Functions

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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


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