Intro to radians and unit circleF-TF.1F-TF.2

ANGLES AND ANGLE MEASURE

FIND THE EXACT VALUE OF THE FOLLOWING.

An angle on the coordinate plane is in STANDARD POSITION if the vertex is at the origin and one ray is on the positive x-axis.

The ray on the x-axis is called the initial side

The ray that rotates about the center is called the terminal side

ANGLES IN STANDARD POSITION

MEASURING ANGLES

You Try: Draw a 150* angleDraw a -45* angle

If the measure of a an angle is positive, the terminal side is rotated counterclockwise

If the measure of an angle is negative, the terminal side is rotated clockwise

A radian is the measure of an angle in standard position with a terminal side that intercepts an arc with the same length as the radius of the circle.

The circumference of a circle is One complete revolution around a circle equals radians.

Since =360*, then =180.

RADIAN – CLICK FOR ANIMATION

Degrees to Radians Radians to Degrees

CONVERTING BETWEEN DEGREES AND RADIANS

Ex:

You try:

Rewrite each degree measure in radians and each radian measure in degree

PRACTICE

SKETCH EACH ANGLE. THEN DETERMINE THE REFERENCE ANGLE

    

  

Get from Shawna

PAPER PLATE ACTIVITY

DEGREES AND RADIANS

REVIEW OF QUADRANT ANGLES

45-45-90 RIGHT TRIANGLE

1

1

45

45

Since this is an isosceles triangle, 2 sides are the same. We will let these congruent sides be 1 and 1.

We can then use the Pythagorean Thm. To find the length of the hypotenuse.

a2+b2=c2

12+12 = c2

2=c2

=c

30-60-90 RIGHT TRIANGLE

60 60

602 2

21 1

3030

Start with an Equilateral Triangle

30

60

2

1Then use Pyth. Thm

a

a2+12=22

a2=3a=

TRIG RATIOS OF SPECIAL ANGLES:

12

12

1

1

HAND TRICK – 1ST QUADRANT

2

PRACTICE PROBLEMS WITH HAND TRICK

worksheet

HOMEWORK