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4.3

Goals: Solve problems involving trigonometric functions. Memorize the 16-Point Unit Circle. 4.3. Trigonometry Extended: The Circular Functions. What you’ll learn about. Trigonometric Functions of Any Angle Trigonometric Functions of Real Numbers Periodic Functions

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4.3

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  1. Goals: Solve problems involving trigonometric functions. Memorize the 16-Point Unit Circle. 4.3 Trigonometry Extended: The Circular Functions

  2. What you’ll learn about • Trigonometric Functions of Any Angle • Trigonometric Functions of Real Numbers • Periodic Functions • The 16-point unit circle … and why Extending trigonometric functions beyond triangle ratios opens up a new world of applications.

  3. Initial Side, Terminal Side

  4. Positive Angle, Negative Angle

  5. Quadrants What do quadrants and the Super Bowl have in common?

  6. Coterminal Angles Two angles in an extended angle-measurement system can have the same initial side and the same terminal side, yet have different measures. Such angles are called____________________.

  7. Example Finding Coterminal Angles

  8. Example Finding Coterminal Angles

  9. Trigonometric Functions of any Angle Let be any angle in standard position and let P(x, y) be any point on the terminal side of the angle (except the origin). Let r denote the distance from P(x, y) to the origin. Then…

  10. Example Evaluating Trig Functions Determined by a Point in QI

  11. Example5: Evaluating More Trig Functions

  12. Example7a: Using one Trig Ratio to Find the Others Find and by using the given information to construct a reference triangle. and

  13. Example7b: Using one Trig Ratio to Find the Others Find and by using the given information to construct a reference triangle. and

  14. Unit Circle The unit circle is a circle of radius 1 centered at the origin.

  15. The 16-Point Unit Circle

  16. Refer to the unit circle shown. Which letter best represents the value given? cos -270° sin π/3 cos 4π/3 sin - 5π/4 tan 60°

  17. Find the exact value of each of the following trig expressions. Try to give the result without looking at your unit circle.

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