Angles and Arcs Lesson 2.1

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

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

Angles Positive Angles Negative Angles Measured counter-clockwise Measured clockwise

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

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

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

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

Arc Length Given a circle with 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 = what is the arc length? S θ r View NSpire Demo

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

Linear and Angular Speed If ω is the angular velocity of a round object with radius r 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?

Assignment Lesson 2.1 Page 130 Exercises 1 – 69 EOO 71,79,83