4.1 Highlights

Question 1

The __ __ is the circle of radius _ centred at the __.

Answer 1

unit circle
1
origin

Question 2

Equation of the unit circle

Answer 2

x^2 + y^2 = 1

Question 3

List all the positive and negative horizontal and vertical axes, their coordinates, and if x or y are greater than or less than 0

Answer 3

positive horizontal axis: points in the coordinate plane of the form (x,0), where x>0

negative horizontal axis: (x,0), x<0

positive vertical axis: (0,y), y>0

negative vertical axis: (0,y), where y<0

Question 4

The radius corresponding to an angle where θ > 0

Answer 4

for θ > 0, the radius of the unit circle corresponding to θ degrees is the radius that has an angle θ degrees with the positive horizontal axis, as measured counterclockwise from the positive horizontal axis

TLDR: when θ > 0, it moves counterclockwise from the axis.

Which one? the positive horizontal axis (x: 0 –> infinity) is the standard starting point for measurement

Question 5

The radius corresponding to an angle where θ < 0

Answer 5

for θ < 0, the radius of the unit circle corresponding to θ degrees is the radius that has angle |θ| degrees with the positive horizontal axis, as measured clockwise from the positive horizontal axis.

Question 6

Angle measurements for a radius on the unit circle are made from the __ ___ __

Answer 6

positive horizontal axis

Question 7

Positive angles correspond to moving ___ from the __ ___ __

Answer 7

counterclockwise

positive horizontal axis

Question 8

Negative angles correspond to moving __ from the __ ___ __

Answer 8

clockwise

positive horizontal axis

Question 9

How does an angle correspond to multiple degrees?

Answer 9

a radius of the unit circle corresponding to theta degrees also corresponds to θ + 360n degrees for every integer n

Question 10

Length of a circular arc

Answer 10

an arc corresponding to theta degrees on a circle of radius r has length (θpir)/(180)

Question 11

Dimensions of a triangle with angles of: 
30 degrees 
60 degrees
90 degrees 
and hypotenuse length of 1

Answer 11

the side opposite of the 30 degree angle has length 1/2

the side opposite of the 60 degree angle has length √3/ 2