Angles and Arcs Lesson 2 1 Angles Extends

Angles and Arcs Lesson 2. 1

Angles ¡ Extends indefinitely Ray Endpoint ¡ Angle l l Formed of two rays Have same endpoint 2

Angles ¡ Angles can be l l l Straight Right Acute Obtuse Obese less than 90° greater than 90° View NSpire Demo 3

Angles ¡ Positive Angles l ¡ Measured counter-clockwise Negative Angles l Measured clockwise 4

Angles ¡ Degree = ¡ Complementary angles l ¡ of a full revolution a + b = 90° Supplementary angles l a + b = 180° 5

Co-terminal Angles ¡ We measure angles in standard position on the coordinate axes θ ¡ This same angle could be 6

Radian Angle Measure ¡ Consider the length of the radius laid out on the circumference θ r r View NSpire Demo The resulting angle θ, is 1 radian ¡ There are radians in a circle ¡ 7

Radian Angle Measure Conversion of radians to degrees ¡ Use this proportion ¡ l ¡ Solve for desired value (degrees or radians) Try it: l l is how many degrees? 135° is how many radians? 8

Arc Length S Given a circle with θ r radius r and central angle = θ radians ¡ The arc length can be calculated by ¡ ¡ Try it: For a circle with radius 3. 5 and θ = View NSpire Demo what is the arc length? 9

Linear and Angular Speed ¡ ¡ Angular speed is radians/unit time Linear speed is linear units / unit time 10

Linear and Angular Speed ¡ If ω is the angular velocity of a round object with radius r l ¡ The linear velocity of a point on the circle is For a 20 ft radius windmill rotating at 10 rpm, what is the linear velocity of the tip of the blade? 11

Assignment Lesson 2. 1 ¡ Page 130 ¡ Exercises 1 – 69 EOO 71, 79, 83 ¡ 12