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Angles and Arcs

Angles and Arcs. Lesson 2.1. Angles. Extends indefinitely. Ray Angle Formed of two rays Have same endpoint. Endpoint. . less than 90°. greater than 90°. Angles. Angles can be Straight Right Acute Obtuse Obese. View NSpire Demo. Angles. Positive Angles

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Angles and Arcs

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  1. Angles and Arcs Lesson 2.1

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

  3. less than 90° greater than 90° Angles • Angles can be • Straight • Right • Acute • Obtuse • Obese View NSpireDemo

  4. Angles • Positive Angles • Measured counter-clockwise • Negative Angles • Measured clockwise

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

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

  7. 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 NSpireDemo

  8. Radian Angle Measure • Conversion of radians to degrees • Use this proportion • Solve for desiredvalue (degrees orradians) • Try it: • is how many degrees? • 135° is how many radians?

  9. Arc Length S • 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? θ r View NSpireDemo

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

  11. Linear and Angular Speed • If ω is the angular velocity of a round object with radius r • The linear velocity of apoint 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?

  12. Assignment • Lesson 2.1 • Page 130 • Exercises 1 – 69 EOO71,79,83

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