Quiz

1) Fill in the sides lengths for the following triangle (and label them hyp, opp, adj):

30º2) Find the compliment, supplement, and 2 coterminal angles for an angle that is 62.5º

1

2

3

OPP

HYP

ADJ

Compliment – 27.5, supplement – 117.5, coterminals 422.5 and -297.5

You can also measure angles in radians.

One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length r.

Since the circumference of a circle is 2πr, there are 2π radians in a full circle.

Degree measure and radian measure are therefore related by the following:

360º = 2π radians

r r

one radian

Conversion Between Degrees and Radians

Use the Proportion:

360 2

x radians

You plug in either the degree or radians that you are given and cross multiply to get the answer

Examples: Change each in radiansa. 240º b. 135º

360 2

x radians

360 2

x radians

240

360 2

r

240(2 ) 360r 480 360r 360 360

4

3r

135(2 ) 360r 270 360r 360 360

3

4r

135

360 2

r

Examples: Change each in radiansa. 240º b. 135º

4

3r

3

4r

What does this mean?

It means that in the first case 240º is equal to radians4

3

And in the 2nd case 135º is equal to

radians

3

4

Examples: Rewrite each in degreesa. 5π 8

360 2

x radians

58

360 2

x

5(2 ) 360

8x

2 1800

1 8

x

1800 16 x 1616

112.5 x

Be careful with the multiplications

Examples: Rewrite each in degreesa. 2π 3

360 2

x radians

23

360 2

x

2(2 ) 360

3x

2 720

1 3

x

720 6 x 66

120 x

The most common conversions

306radians

454radians

603radians

902radians

180radians

2 360radians

We will add several more to this chart next class so leave some room