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Warm-Up Question

Warm-Up Question. Solve each triangle. B. B. 10.8. 5. a. a. A. A. b. C. C. b. Definition of General Angles and Radian Measure. Trigonometric Ratios and Functions. Angles in Standard Position. Lesson: P.563. In a coordinate plane, an angle can be formed

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Warm-Up Question

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  1. Warm-Up Question Solve each triangle. B B 10.8 5 a a A A b C C b

  2. Definition of General Anglesand Radian Measure Trigonometric Ratiosand Functions

  3. Angles in Standard Position • Lesson: P.563 In a coordinate plane, an angle can be formed by fixing one ray, called the initial side, and rotating the other ray, called the terminal side, about the vertex. An angle is in standard position if its vertex is at the origin and its initial side lies on the positive x-axis. terminal side initial side • Example: P.563 Draw an angle with the given measure in standard position. Required Practice: P.566 3, 4, 6, 7, 8, 9, 14

  4. Coterminal Angles • Lesson: P.564 The angle and are coterminal because their terminal sides coincide. An angle coterminal with a given angle can be found by adding or subtracting multiples of . • Example: P.564 Draw an angle with the given measure in standard position. Then find one positive coterminal angel and one negative coterminal angle. Required Practice: P.567 15, 16, 17, 18

  5. Warm-Up Question Find the circumference and area of below circle. Circumference: Area of Circle: 5 Find the arc length and area of below sector. Arc Length: 5 Area of Sector:

  6. Radian Measure • Lesson: P.564 One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length r. (Refer to the animation on the next slide.) There are approximately 6.28 radian in a full circle, or to be exact. Degree measure and radian measure are therefore related by the equation radians, or . r r 1 radian • Example: P.564 Convert to radians. Convert to degrees. Required Practice: P.565 5, 6, 7, 8

  7. Radian Measure

  8. Arc Length and Area of a Sector • Lesson: P.565 The arc length s and area A of a sector with radius r and central angle (measured in radians) are as follows. Arc Length: Area: sector r arc length s central angleθ • Example: P.567 Find the arc length and area of a sector with the given radius r and central angle . 1) r = 4 in., 2) r = 15 cm, Required Practice: P.56733, 37

  9. Homework Part 1 Workbook P.116: 1, 4, 5 Part 2 Workbook P.116 – 117: 6, 7, 8, 9, 10, 11, 13, 14

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