4 1 Degrees and Radians Angle in Standard

4. 1 Degrees and Radians

Angle in Standard Position Initial side is from the 0 0. initial center to 0

Angle in Standard Position Then draw the 0 initial terminal side terminal

Label a circle with degrees 0 90 0 0 + 135 45 0 0 0 180 0 225 0 270 0 315

Negative direction - clockwise -270 0 -90 0 -45 - 0 -180

More than 0 360 0 720 (360 n)

More than 0 360 90 450 (360 n + 90) 180 540 0 720 (360 n)

Coterminal Angles end at the same place 0 60 60 -360 0 420 60+360 0 -300

Coterminal Angles end at the same place /3 /3 + 2 7 /3 /3 -2 - 5 /3

Circumference Unit Circle C=2 r If radius is 1 1 C = 2 (1) C=2

C= 2 Лr C= 2 Л 360 degrees same as 2 Л radians 1

Radian measure of an angle is the arc 1 length of a unit circle.

Think of 2 Л on a ruler or number line. 1 0 Л/2 Л 3. 14 1. 57 2 Л 6. 28

1 Radian is NOT the same as 1 Л radians. 0 180 0 1 1 Л 1 Л 2 Л 3. 14 6. 28

Now wrap the number line around the unit circle 2 Л Л 0

Where is Л ? Where is 2 Л ? Where is Л/2 ? Where is 3 Л/2 ? Where is Л/4 ?

Radian Measure 2 Л ? Л/2 Л/4 Л Л 0, 2 Л Л/2 3 Л/2 Л /4 3 Л /2

1 Radian = 0 57. 3 Like 1” on the ruler

Locate Quadrants 0 100 II 0 100 0 200 III 2 Л/3 II I 2/3 Л II 0 200 III IV - Л/4 - Л /4 IV

To change degrees to radians Multiply by Л 180

0 30 Change to Radians. 30 Л = Л 180 6 Cancel fractions.

To change radians to degrees Multiply by 180 Л

Change ¶ to degrees. 3 Л x 180 0 = 60 3 Л

Change R 1 to Degrees 1 x 180 = Л 3. 14 Not the same as 0 1 Л = 180 0 57. 3

Proportions can also be u 0 Change 20 to Rad 0 180 0 20 = R 1 Л 20 1 Л = R 180 Л 9

Calculator mode. Be sure your settings are correct.

MEMORIZE 0 360 0 180 0 90 0 45 0 30 2 Л Л Л /2 Л /4 Л /6

MEMORIZE 0 60 0 120 0 150 0 135 0 270 Л /3 2 Л /3 5 Л /6 3 Л /4 3 Л /2

Multiples of Л/4 0 are multiples of 45. Multiples of Л/6 are muliples of 0 30

Find a complementary angle to Л/5 Л/2 - Л/5 5 Л/10 - 2 Л/10 = 3 Л/10

Find a supplementary angle to Л/5 Л - Л/5 5 Л/5 - 1 Л/5 = 4 Л/5

A revolution is another unit for measuring rotations.

1 revolution = direction is counterclockwise 0 360

How much is 1/2 revolution? 1/2 * 360 = 0 180

How much is 2/3 revolution? 2/3 * 360 = 0 240

How many revolutions equal 10 radians? Change radians to degrees

10 radians = ? revol. 10 * 1800 0 = = 573 Л 3. 14 Changed radians to degrees

Now change revolutions 0 573 to 360 x = 573 = 1. 59 360 rev

Different method 1 rev x rev = 2 Л rad 10 rad cross multiply

STUDY ! ! ! !

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