Chapter 7 Section 7.1 Angles
One Degree
1/360 or a circular rotation
Measure of An Angle
the amount of rotation from the intial side to the terminal side, is known as?
Quadrantal Angle
a special type of angle that has a terminal side that lies on an axis, this angle can have a measure of 0, 90, 270, or 360 -- degrees.
Inital Side
the fixed ray in an angle
Circumference of a Circle (2pir)
the length of an arc around an entire circle is called?
Yes. It is approximately 57.3°. Because 2π radians equals 360°, 1 radian = 360/2π (reducing then dividing we get 57.3)
A measure of 1 radian looks to be about 60°. Is that correct?
Positive Angle
An angle that is being measured from its inital side to its terminal side in a counter clock wise manner is called a _________________ angle.
Find the reference angle of 225°
Because 225° is in the third quadrant, the reference angle is ∣(180° − 225°)∣ = ∣−45°∣ = 45°
The Ration of Circumference to Radius
C/r = 2pi
1. If necessary, convert θ to radians. 2. Multiply half the radian measure of θ by the square of the radius r : A = 1/2 θ r^2.
Given a circle of radius r, find the area of a sector defined by a given angle θ, what are the steps?
v = r/w
When the angular speed is measured in radians per unit time, linear speed and angular speed are related by
Angle Measure (in radians)
arc length / radius, equals?
multiply 3pi/4 (radians by 180/pi)
how do you find the exact degree measure of 3pi/4 (radians)
A full rotation of any circle is 2pir so 2pir * 1/3 = s (the arc length) and radian measure = s/r so 2pir/3/r = the radian measure, which is 2pi/3
how do you find the radian measure of one-third of a full rotation?
multiply 54 by pi/180 (But really just divide 54/180 and leave the result * pi /result)
how do you get the radian measure of 54 degrees?
Standard Position
if an angle's vertex is located at the orgin and its inital side extends along the positive x-axis, what position is it in?
90 degrees (90/360 = 1/4)
if the terminal side measures 1/4 of the way around a cicle and is moving counter clock wise from the positive x-axis, how many degrees is that angle?
Coterminal Angles (every angle greater than 360 or less than 0 degrees)
if two angles have the same terminal side they
30/360 (degrees) = 1/12 = 1/3(1/4)
if you were to draw an angle of 30 degrees in standard position within a circle, how would you know where to draw the terminal side?
angular speed
is angular rotation per unit time
Angle
is created when two rays have a common end point, known as the vertex.
Linear speed
is speed along a straight path and can be determined by the distance it moves along (its displacement) in a given time interval.
Arc Length
radius * angle measure, equals?
Terminal Side
the ray that rotates in an angle, creating different angle measures.
Linear Speed
v = s/t where v equals linear speed, s equals displacement and t equals time
angular speed
w = theta/ t, where ω (read as omega) is angular speed, θ is the angle traversed, and t is time.