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Lesson 9.2 Define General Angles and Use Radian Measure

Lesson 9.2 Define General Angles and Use Radian Measure. Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up. Lesson Presentation. Lesson Quiz. Warm-Up. Write the expression in simplest form. 1. 2. 3. 4.

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Lesson 9.2 Define General Angles and Use Radian Measure

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  1. Lesson 9.2Define General Angles and Use Radian Measure Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up Lesson Presentation Lesson Quiz

  2. Warm-Up Write the expression in simplest form. 1. 2. 3. 4. 5.A compact disk has radius 6 centimeters. Find its circumference and area to the nearest tenth. Circumference is , Area is

  3. Vocabulary Angle in Standard Position: Angle with its vertex at the origin and its initial side on the positive x-axis. Terminal side is the end of your angle rotation. Coterminal Angles: An angle is coterminal with a given angle if the sum or difference is a multiple of . Radian: It is the measure of an angle in standard position whose terminal side intercepts an arc of length r. Radian Measure: Circumference of a circle is , therefore there are radians in a circle. Degree measure and radian measure are related by the equation radians.

  4. Vocabulary Arc Length: Degrees: Radians: Area of a Sector: Degrees: Radians:

  5. Essential Understandings What is positive and negative measure? • Angles with positive measure result from counterclockwise rotation. Angles with negative measure result from clockwise rotation.

  6. 1 EXAMPLE Draw angles in standard position Draw an angle with the given measure in standard position. 1. 2. 3. 4.

  7. 2 EXAMPLE Find coterminal angles Find one positive angle and one negative angle that are coterminal with the angle. SOLUTION 1. 2.

  8. 3 EXAMPLE Convert between degrees and radians Convert the given angle measure. SOLUTION radians to - degrees 1. to radians

  9. Vocabulary

  10. 4 EXAMPLE Solve a real – world problem Camp KIS Children at KIS day camp are playing a game on a circular area. The shaded sector in the figure is called the “safe zone”, and is marked off by rope along its outer edge. Find the length of the rope and the area of the safe zone in radians. Arc Length: Arc Area: ft. The approximate Length of the rope is 37.7 ft. and the area of the safe zone is 339 .

  11. Lesson 9.2 Homework: • Practice B • Practice C “Honors”

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