Week 1

Question 1

what is an angle?

Answer 1

the joining of two rays, having a common endpoint (vertex)

Question 2

angle have direction?

Answer 2

the angle begins with the initial side (ray) and rotates toward the terminal side

Question 3

counter/clockwise angle measures

Answer 3

angles rotating counterclock are positive and clockwise are negative

Question 4

standard position?

Answer 4

the initial side at the x axis and the vertex at the origin of the xy axes

Question 5

quadrantal angle

Answer 5

angle where the terminal side lies on an axis
each angle is a multiple of 90

Question 6

coterminal angles

Answer 6

two angles in standard position with the same terminal side
every angle >360 or <0 is coterminal with any angle between 0-360

Question 7

radians

Answer 7

the angle where the radius (r) equals the arc (s) formed by the initial and terminal sides
equal to the arc length divided by the radius
*are unitless

Question 8

30 degrees in radians (and coordinates)

Answer 8

pi/6
(root 3/2) , (1/2)

Question 9

45 degrees in radians (and coordinates)

Answer 9

pi/4
(root 2/2) , (root 2/2)

Question 10

60 degrees in radians (and coordinates)

Answer 10

pi/3
(1/2) , (root 3/2)

Question 11

arc length?

Answer 11

arc length (s) = radius (r) x theta (radians)

Question 12

area of a sector

Answer 12

A = 1/2 (theta) (radius squared)
*theta is in radians

Question 13

angular speed

Answer 13

angular speed is the change in angular rotation of a point moving along the circumference of a circle of radius r, per unit of time

(lower case omega) = theta (radians) / time (t)

(change in theta over change in time)

Question 14

linear speed

Answer 14

change in distance over change in time
v = s (arc length) / time (t)

can also be found by (v = r (angular speed))

Question 15

ray

Answer 15

a directed line segment
a starting point called the endpoint and all other points extending from that point in a specific direction