TOPIC: Measurement of Angles



TOPIC: Measurement of Angles

An angle is said to be in standard position if

1) its vertex is at the origin

2) its initial side is on the positive x-axis.

terminal

side

[pic]

initial side

A counterclockwise rotation represents a positive angle.

A clockwise rotation represents a negative angle.

The amount of rotation is measured in degrees or radians.

DEGREE MEASURE

1 degree = [pic] of a rotation.

Acute angle=_____________________________________

Right angle=_____________________________________

Obtuse angle=____________________________________

Straight angle=____________________________________

RADIAN MEASURE:

The radian measure of an (AOB is the number of radius units in the length of arc AB

[pic]

[pic]=[pic]

1. Find [pic] in radians. 2. So, if s = r, find [pic].

[pic]

[pic] = [pic]

3. Convert - 225( to radians. Leave in terms of (.

4. Convert 200( to radians. Round to three decimal places.

5. Convert -(/3 to degrees.

6. Convert 3.41 radians. Round to the nearest tenth of a degree.

Find the complement or supplement of each angle.

7. Find the complement of a 46[pic] angle.

8. Find the supplement of a 124[pic] angle.

9. Find the complement of [pic].

10. Find the complement of [pic].

11. Find the supplement of [pic].

12. Find the supplement of [pic].

13. Find the complement of [pic].

Sketch these angles:

1. Sketch a 120( angle, - 120( angle

2. Sketch a [pic] radians angle, - [pic] radians angle

-----------------------

N1-1

[pic]

A

s

r

B

s

3

r

2

1 radian = measure of a central angle whose arc has length r.

Formulas:

Degrees to Radians:

Radians to Degrees:

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