Academy Algebra II/Trig

Pre-Calculus (4.1)7.1: Angles and Their MeasureHW tonight: p.513 (11-22 all) HW tomorrow: p.513 (24-62 even)

Angles The initial side of an angle coincides with

the positive x-axis. Positive angles are generated by a

counterclockwise rotation and a negative angle by a clockwise rotation.

Coterminal Angles Angles with the same initial and terminal

sides are coterminal angles.

Alpha and beta arecoterminal angles.

Radian Measure One radian is the measure of a central

angle that intercepts an arc s equal in length to the radius r of the circle.

r

r rs

Radian Measure Because the circumference of the circle is

, it follows that a central angle of one full revolution corresponds to an arc length of . Therefore, radians corresponds to .

r2

r2 2360

2

Radian Measure Other common angles:

4

6

2

3

Identify the Following angles:

0, , , and .2

3 2

Determine the quadrant in which the angle lies. (The angle is given in radian measure.)

1.) 2.)

3.) -1 4.) 5.63

5.) 6.)

4

75

4

10

12

7

Sketch the angle in standard position. Determine two coterminal angles in radian measure (one positive & one negative) for the given angle.

1.)

2.)

2

7

6

5

Sketch the angle in standard position. Determine two coterminal angles in radian measure (one positive & one negative) for the given angle.

3.)

4.)

4

7

3

2

Determine the quadrant in which the angle lies.

1.) 2.)

3.) 4.)

9.7 5.275

25.260 4.2

Sketch the angle in standard position. Determine two coterminal angles in degree measure (one positive & one negative) for the given angle.

1.)

2.)

120

270

Find (if possible) the complement and supplement of the angle.Two positive angles are complementary

if their sum is . Two positive angles are supplementary if their sum is .

1.) 2.)

3.) 3 4.) 1.5

2

12

6

5

Find (if possible) the complement and supplement of the angle.

1.) 2.)

3.) 4.)

87 167

130 52

Do Now: Sketch the angle in standard position. Determine two coterminal angles in degree measure (one positive & one negative) for the given angle.

1.)

2.)

114

445

Convert degrees to radians

rad180

1

180rad 1

Express the angle in radian measure as a multiple of pi. 1.) 2.)

3.) 4.)

315 120

270 144

Convert the angle measure from degrees to radians. Round your answer to three decimal places. 1.) 2.)

52.46 7.83

Express the angle in degrees.

1.) 2.)

3.) 4.)

12

7

9

6

1515

28

Convert the angle measure from radians to degrees. Round your answer to three decimal places. 1.) 2.) 4.8

13

8

Convert the angle to decimal form.60 minutes = 1 degree60 seconds = 1 minute

1.) 2.) 3.)'10275 '129 "36125

"'SMD

Convert the angle to form.60 minutes = 1 degree60 seconds = 1 minute

1.) 2.)75.310 12.345

"'SMD

Do Now: Round your answers to three decimal places. Convert the angle measure from degrees to radians. 1.) 2.)

3.) 4.) -0.48

54.0 395

5.6

Convert the angle measure from radians to degrees.

Convert the angle to form.60 minutes = 1 degree60 seconds = 1 minute

3.) 4.) 355.0

"'SMD

7865.0

Arc Lengthradians.in measured is wherers

240

4r

radians 3

4240

76.163

16

3

44

s

s

rs

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.1.) r = 22 feet, s = 10 feet

2.) r = 80 km, s = 160 km

Find the length of the arc on a circle of radius r intercepted by a central angle of .1.) r = 9 feet,

2.) r = 40 cm,

60

radians 4

3