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Math III Accelerated

Math III Accelerated. Chapter 13 Trigonometric Ratios and Functions. Warm Up 13.2. Write the expression in simplest form. 13.2 Define General Angles and Use Radian Measure. Objective: Use general angles that may be measured in radians. Angles in Standard Position.

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Math III Accelerated

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  1. Math III Accelerated Chapter 13 Trigonometric Ratios and Functions

  2. Warm Up 13.2 • Write the expression in simplest form.

  3. 13.2 Define General Angles and Use Radian Measure • Objective: • Use general angles that may be measured in radians.

  4. Angles in Standard Position • In the coordinate plane, an angle can be formed by fixing one ray, called the _______________ side, and rotating the other ray, called the ____________________ side, about the ____________________. • An angle is in standard position if its vertex is at ___________ and its initial side lies on the positive ____________________ .

  5. Positive and Negative Angles • A positive angle opens _________________. • A negative angle opens _________________.

  6. Example 1 • Draw a 405˚ angle in standard position. • Draw a –65˚ angle in standard position.

  7. Coterminal Angles • Angles that share the same terminal side are called coterminal angles. • Coterminal angles can be found by adding (or subtracting) multiples of 360˚ to (from) the given angle.

  8. Example 2 • Find one positive and one negative angle that are coterminal with 210˚. Sketch your results.

  9. Checkpoints 1 & 2 • Draw an angle with the given measure in standard position. Find one positive and one negative coterminal angle. • 485° • –75°

  10. Radian Measure • Angles can be measured either in degrees or in radians.

  11. Converting Between Degrees and Radians • Degrees to Radians Radians = Degrees • • Radians to Degrees Degrees = Radians •

  12. Example 3 • Convert : • 315˚ to radians • π/6 radians to degrees

  13. Checkpoints 3 & 4 • Convert the degree measure to radians or the radian measure to degrees. • 200˚ • π/5

  14. Sectors of Circles • A sector is a region of a circle that is bounded by two radii and an arc of the circle. • The central angle θof a sector is the angle formed by the two radii. r θ r

  15. Arc Length and Area of a Sector • The arc length s and areaA of a sector with radiusr and central angleθ (measured in radians) are: • Arc Length s = r θ • AreaA = ½ r2 θ s θ r

  16. Example 4 • Find the arc length and area of a sector with a radius of 15 inches and a central angle of 60˚.

  17. Checkpoint 5 • Find the arc length and area of a sector with a radius of 5 feet and a central angle of 75˚.

  18. Homework 13.2 • Practice 13.2

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