Radians and Angles

Radians and AnglesWelcome to Trigonometry!!

Starring

The Coterminal Angles

Supp & Comp Angles

The Converter

And introducing…

Angles

Rad Radian

Degree

THE UNIT CIRCLE

1

0.5

-0.5

-1

-2 -1 1 2

You & I are gonna be great

friends!

Angle- formed by rotating a ray about its endpoint (vertex)

Initial Side Starting position

Terminal Side Ending position

Standard PositionInitial side on positive x-axis and the vertex is on the origin

Angle describes the amount and direction of rotation

120° –210°

Positive Angle- rotates counter-clockwise (CCW)

Negative Angle- rotates clockwise (CW)

1 Radian = measure of central angle, , that intercepts the arc that has the same length as the radius of the circle

Length BC on AB = 4.31 cm

m AB = 4.31 cm

A B

C

Arc length “s” = radius when = 1 radian

Calculate the number of radians in one full circle:

1

0.5

-0.5

-1

-2 -1 1 2

C = r2

r

s

radius

length arc

radians 22 r

r

0

3.14

0, 2

0, 6.28

571.12

712.42

3

Therefore, we can say that 1 full revolution = 2 radians.

Coterminal Angles: Two angles with the same initial and terminal sides

Find a positive coterminal angle to 20º 38036020

34036020

Find 2 coterminal angles to 4

15

4

8

4

15

24

15

4

8

4

15

24

15

4

23

4

8

4

7

Find a negative coterminal angle to 20º

4

Now, you try…

Find two coterminal angles (+ & -) to 3

2

What did you find?

3

8,

3

4

These are just two possible answers. Remember…there are more!

Complementary Angles: Two angles whose sum is 90

Supplementary Angles: Two angles whose sum is 180

6

62

36

2

66

3

3

2

3

233

2

3

3

To convert from degrees radians, multiply by

To convert from radians degrees, multiply by

180

180

Convert to radians:

180

135

4

3

180

80

9

4

To convert from degrees radians, multiply by

To convert from radians degrees, multiply by

180

180

Convert to degrees:

180

3

8 480

180

6

5 150

So, you think you got it now?

1 degree = 60 minutes

1° = 60

1 minute = 60 seconds

1 = 60

So … 1 degree = _________seconds

3600

Express 365010as decimal degrees

3660

50

3600

10

8361.3636 + .8333 + .00277

OR Use your calculator!! Express 365010as decimal degrees

Enter 36

Press this button ’ ’’Press enter

Enter 50

Press this button ’ ’’Go over to the ’ symbol -- enter

Enter 10Press this button ’ ’’Go over to the ’’ symbol -- enterPress enter

Convert 50 47’ 50’’ to decimal degree

50.7972

Convert 125 27’ 6’’ to decimal degree

125.4517

Can you go backwards and convert the decimal degree to degrees minutes seconds?

Enter 125.4517 Go to DMS hit enter.

Express 50.525 in degrees, minutes, seconds

50º + .525(60) 50º + 36.5

50º + 36 + .5(60)

50 degrees, 36 minutes, 30 seconds