Unit 6 Day 1December 12th

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Sit on your paper plate!

Take markers, ruler, 1 pipe cleaner and protractor.

Do not bend the pipe cleaner.

OBJECTIVES TODAY both in degree and radian measure…

1. Terminology.

2. Sketch angles in standard position.

3. Sketch/find co-terminal angles.

4. Sketch/find reference angles.

5. Create the “unit circle”.

4.1 Angles

• An Angle is determined by the _________________ of a ray about its __________.

• The starting position of the ray is the _______________ side.

• The position after the rotation is the ________________ side.

Initial side

Terminal side

You can not determine which is the initial or terminal side without showing the rotation

An angle is in Standard Position angle if

• Initial side is along _______________ x - axis.

• Vertex is at the ____________

The ___________________________ is

determined by the amount of rotation from

the ____________________ to the

__________________.

Standard Position & Quadrants

positive x-axisorigin 0o

90o

180o

270o

360o

III

III IV

Paper Plate Unit Circles

1) Fold plate into quarters.

2) Draw in and label axes.

3) Label the quadrants.

4) Label +/- signs for each quadrant.

5) Using pencil, draw in the circle at the bend in the plate. (approx. 1 ½ inches from outside)

Paper Plate Unit Circles

6) Label positive degree angles at 0, 90, 180, 270, 360 near the penciled in circle.

7) Using a protractor mark off and label angles of: 30o, 45o, 60o, 120o, 135o, 150o, 210o, 225o, 240o, 300o, 315o, 330o.

• If the rotation is counterclockwise the angle is ________________________.

• If the rotation is clockwise the angle is ___________________.

Another way to measure angles is with

_______________

Radian Measure

There are ____ radians in one complete revolution of a circle.

Therefore……

360 degrees = ____ radians

Standard Position & Quadrants

positive x-axisorigin 0o

90o

180o

270o

360o

III

III IV

2R

R

0 ,2R R

3

2R

Paper Plate Unit Circles

Label the angles in radian measure.

Co-Terminal Angles

Co-terminal angles are angles in standard position that have the same _______________________________

Find 1 positive and 1 negative angle Co-Terminal with the given

angle.Add or subtract 360o .

1) 40o

2) -390o

3) 137o

Find 1 positive and 1 negative angle Co-Terminal with the given

angle.2 radiansAdd or subtract

Be sure to get a common denominator with the radians.

4)

5)

6)

6radians

2

3radians

2.5radians

Reference Angles

Definition: For any angle (theta) that is in standard position, the reference angle…

1) Is acute

3) Has one side on the x-axis

4) Uses the terminal side of the given angle

2) Is positive

Steps to draw the reference angle

1) Draw in the given angle w/ rotation

2) Connect the tip of the terminal side of the given angle to the x-axis. (mark it perpendicular to the x-axis)

3) The reference angle is the CENTRAL ANGLE formed by the right triangle.

The PINK angle is the reference angle.

From the x-axis to the terminal side of the given angle.

Ref = givenRef = 180 - given

Ref = 360 - given

Ref = given - 180

These rules are for positive angles only!

Sketch the given angle. Draw in the reference angle. Determine the measure of the reference

angle.

7) 97o

8) 192o

Sketch the given angle. Draw in the reference angle. Determine the measure of the reference

angle.

9) 300o

10) 5

6R

Paper Plate Unit Circles

8) Using a ruler, connect the origin to each of the angles you measured in quadrant I.

9) Put the pipe cleaner through the origin. Bend it in half. Twist the ends together.