Radian Measure That was easy What does that mean? One radian is the measure of a central angle of a circle that intercepts an arc whose length equals a radius of the circle. Central angle intercepts an arc whose length, s, is inches in a circle that has a radius length of 12 inches. Find r = 12 General Formula or or That was easy

Converting from Degrees to Radians To change from degrees to radians, multiply the number of degrees by Convert the following angle measurements from degrees to radians.

Converting from Radians to Degrees To change from radians to degrees, multiply the number of radians by Convert the following angle measurements from radians to degrees.

Comparing Degrees and Radians The radius of a circle is 12 centimeters. What is the number of centimeters in the length of the minor arc intercepted by a central angle that measures 135o? Method 1 Method 2 r = 12 s How about that. You get the same answer either way.

Homework Page 404 - 405: 4 – 22 Even Numbers

Angles in Standard Position Let’s look at a diagram that will explain what an angle in standard position is. y If the terminal side rotates in a counterclockwise direction, the angle is positive. Terminal Side -x x Initial Side If the terminal side rotates in a clockwise direction, the angle is negative. -y

Drawing Angles in Standard Position Draw the following angles. 360o 180o 270o

Reference Angles The reference angle is the acute angle whose vertex is the origin and whose sides are the terminal side of the original angle and the x-axis. The reference angle is denoted as Quadrant I Quadrant II Quadrant III Quadrant IV

Finding Reference Angles For each angle given in radian measure, find the measure of the reference angle in radians. That was easy

Coterminal Angles A positive angle and a negative angle are coterminal angles if the sum of the absolute values of their degree measures is 360 or a multiple of 360. y Example 1 A rotation angle measures 210o. What is the measurement of its coterminal angle? -x x Example b A rotation angle measures 300o. What is the measurement of its coterminal angle? -y

Also name the Coterminal Angle for each angle Homework Page 405: 23 -27 All Also name the Coterminal Angle for each angle

Comparing Degrees and Radians The radius of a circle is 12 centimeters. What is the number of centimeters in the length of the minor arc intercepted by a central angle that measures 135o? Method 1 Method 2 r = 12 s How about that. You get the same answer either way.

Arc Length and Radians

Homework Page 405: 28 – 40 Even Numbers