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Section 6.3 Trigonometric Functions of Angles

Chapter 6 – Trigonometric Functions: Right Triangle Approach. Section 6.3 Trigonometric Functions of Angles. Let POQ be a right triangle with an acute angle  where  is in standard position. The point P is on the terminal side of . P ( x , y ). y. r. y. . x. x. Q. O.

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Section 6.3 Trigonometric Functions of Angles

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  1. Chapter 6 – Trigonometric Functions: Right Triangle Approach Section 6.3 Trigonometric Functions of Angles 6.3 - Trigonometric Functions of Angles

  2. Let POQ be a right triangle with an acute angle  where  is in standard position. The point P is on the terminal side of . P(x, y) y r y  x x Q O 6.3 - Trigonometric Functions of Angles

  3. Definition of Trigonometric Functions • Let  be an angle in standard position and let P(x, y) be a point on the terminal side. If is the distance from the origin to the point P(x, y), then 6.3 - Trigonometric Functions of Angles

  4. Quadrantal Angles • Quadrantal Angles are angles that are coterminal with the coordinate axis. 6.3 - Trigonometric Functions of Angles

  5. Remember:Signs of the Trig Functions Quad Positive Functions Negative Functions I All None II sin, csccos, sec, tan, cot III tan, cot sin, csc, cos, sec IV cos, sec sin, csc, tan, cot 5.2 - Trigonometric Function of Real Numbers

  6. Examples – pg. 460 • Find the quadrant in which  lies from the information given. 6.3 - Trigonometric Functions of Angles

  7. Reference Number • Let be an angle in standard position. The reference angle`associated with is the acute angle formed by the terminal side of  and the x-axis. 5.1 - The Unit Circle

  8. Evaluating Trig Functions for Any Angle • To find the values of the trigonometric functions for any angle , we carry out use the following steps: • Find the reference angle` associated with the angle . • Determine the sign of the trigonometric function of  by noting the quadrant in which  lies. • The value of the trigonometric function of  is the same, except possibly for sign, as the value of the trigonometric function of`. 5.1 - The Unit Circle

  9. Examples – pg. 459 • Find the reference angle for the given angle. 6.3 - Trigonometric Functions of Angles

  10. Examples – pg. 459 • Find the exact value of the trigonometric function. 6.3 - Trigonometric Functions of Angles

  11. Fundamental Identities • Reciprocal Identities • Pythagorean Identities 5.2 - Trigonometric Function of Real Numbers

  12. Examples – pg. 460 • Write the first trigonometric function in terms of the second for  in the given quadrant. 6.3 - Trigonometric Functions of Angles

  13. Examples – pg. 460 • Find the given values of the trigonometric functions of  from the information given. 6.3 - Trigonometric Functions of Angles

  14. Area of a Triangle • The area A of a triangle with sides of length a and b with included angle  is 6.3 - Trigonometric Functions of Angles

  15. Examples – pg. 460 6.3 - Trigonometric Functions of Angles

  16. Examples – pg. 460 6.3 - Trigonometric Functions of Angles

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