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# ET 4.1: Fill in as much of the unit circle as you can. (Degrees, Radians, Coordinates.) - PowerPoint PPT Presentation

ET 4.1: Fill in as much of the unit circle as you can. (Degrees, Radians, Coordinates.). I. II. III. IV. Degrees Radians. 5. 6. 20. Convert from minutes to hours. 1. h rs. 1. 40 min. = 2/3 hrs. 60. min. Sketch the angle. Initial Side. Terminal Side. 1.57. 3.14.

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ET 4.1: Fill in as much of the unit circle as you can. (Degrees, Radians, Coordinates.)

I

II

III

IV

5

6

20

Convert from minutes to hours.

1

hrs.

1

40 min.

= 2/3 hrs.

60

min.

Sketch (Degrees, Radians, Coordinates.) the angle

Initial Side

Terminal Side

1.57

3.14

Definition: Two angles are (Degrees, Radians, Coordinates.)coterminal if they have the same initial and terminal side.

Find coterminal angles to

Two angles are complementary if their sum is (Degrees, Radians, Coordinates.)

Find the complement to

Two angles are supplementary if their sum is (Degrees, Radians, Coordinates.)

Find the supplement to

Convert to a decimal in degrees. (Degrees, Radians, Coordinates.)

Convert to . (Degrees, Radians, Coordinates.)

(.256)(60)

21

15.36

(.36)(60)

21.6

~22

5

4

• Day 1: 7, 12, 13, 19, 21, 33, 39, 43, 47, 53, 55, 61, 65, 69, 73, 75, 81, 85, 89, 91

• Day 2: 8, 103, 104, 105, 107, 117

ET 4.1c

Linear Speed: Object moving along a circle w/ radius r

s = distance object travels

t = time traveling

v = linear speed

Example: in/sec

Linear Speed:

= angular speed “omega”

r = radius of circular motion

v = linear speed (Don’t need radian label; it’s implied.)

Angular Speed (Degrees, Radians, Coordinates.): # of times object can go around per time.

= angular speed “omega”

= central angle measured in radians “theta”

t = time

Note:

Example: rev/min.

The second hand of a clock is 10.2 cm long. Find the linear speed of the tip of this second hand as it passes around the clock face.

s = distance object travels

S =

t = time traveling

Time required to travel this distance would be one minute.

t = 1 minute = 60 seconds

A Ferris wheel with 50-foot radius makes 1.5 revolutions per minute. Find the angular speed of the Ferris wheel in radians per minute and the linear speed.

What is the label you are looking for?

1.5 rev/min is angular speed

S = distance object travels

S = 1.5 revolutions =

t = time to travel 1.5 rev

t = 1 minute

Assignment 4.1 minute. Find the angular speed of the Ferris wheel in radians per minute and the linear speed.

• Day 1: 7, 12, 13, 19, 21, 33, 39, 43, 47, 53, 55, 61, 65, 69, 73, 75, 81, 85, 89, 91

• Day 2: 8, 103, 104, 105, 107, 117