13.2 – Define General Angles and Use Radian Measure

0°

90°

180°

270°

Initial side

Terminal side

Standard Position: Vertex at origin and initial side is on x-axis

1. Draw an angle with the given measure in standard position

65°

65°

1. Draw an angle with the given measure in standard position

230°

230°

40°

50°

1. Draw an angle with the given measure in standard position

495°

135°45°

45°

1. Draw an angle with the given measure in standard position

–60°

60°

Radian: Measure of an angle in standard form whose terminal side intercepts an arc of length r

C = 2πr

So there are 2π radians in a circle

Converting Degrees and Radians

degree180

180

radians

Degrees Radians Radians Degrees

2. Convert the degree into radians.

30°

30180

degree180

60

radians6

135°

135180

degree180

4

3radians

4

3

3. Convert the radians into degrees.

180

10

18

180radians

10

18°

5 180

4

45

180radians

5

4

–225°

0

π2

π

3π 2

45°

π4

135°

3π 4

315°225°

5π 4

7π 4

2π

0

π2

π

3π 2

30°

π6

120°5π 6

300°

150°

7π 6

11π 6

60°

π3

2π

2π 3

4π 3

5π 3

330°240°

210°

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

sin 30°

30°

12

3

=1

2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

cos 45°

45°1

1 2

=1

2

2

2 2

2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

tan 30° =1

3

3

3 3

3

30°

12

3

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

csc 60° =1

32

60°1

23

1

sin 60

21

3 2 3

3

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

sec 60° =112

60°1

23

1

cos60

211

2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

cot 45° =111

1

tan 45

111

1

45°1

1 2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

= 3

2cos

6

6

1 2

3

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

=sin4

4

1

1

2

1

2

2

2 2

2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.

=csc3

3

1

23

=1

32

1

sin3

2

3 2 3

3

5. Evaluate the following trigonometric functions with a calculator. Round answers to four decimal places. Remember to change the mode of your calculator.

sin 55° 0.8192

cos 135° – 0.7071

sec 315° 1.4142=1

cos315

cot 76° 0.2493=1

tan 76

5. Evaluate the following trigonometric functions with a calculator. Round answers to four decimal places. Remember to change the mode of your calculator.

0.4816tan7

2.9238csc9

0.58784

sin5

=1

sin9

–22

sec3

=

12

cos3