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Section 5.2 Trigonometric Function of Real Numbers

Chapter 5 – Trigonometric Functions: Unit Circle Approach. Section 5.2 Trigonometric Function of Real Numbers. Definition of the Trig Functions. Example – pg. 384.

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Section 5.2 Trigonometric Function of Real Numbers

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  1. Chapter 5 – Trigonometric Functions: Unit Circle Approach Section 5.2 Trigonometric Function of Real Numbers 5.2 - Trigonometric Function of Real Numbers

  2. Definition of the Trig Functions 5.2 - Trigonometric Function of Real Numbers

  3. Example – pg. 384 • Find sin t and cost for the values of t whose terminal points are shown on the unit circle in the figure. t increases in increments of /4. 5.2 - Trigonometric Function of Real Numbers

  4. Special Values 5.2 - Trigonometric Function of Real Numbers

  5. Domains of the Trig Functions Function Domain sin, cos All real numbers tan, sec All real numbers other than for any integer n cot, csc All real numbers other than n for any integer n 5.2 - Trigonometric Function of Real Numbers

  6. 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

  7. Example – pg. 384 • Find the exact value of the trigonometric functions at the given real number. 5.2 - Trigonometric Function of Real Numbers

  8. Examples – pg. 385 • Find the sign of the expression if the terminal point determined by t is in the given quadrant. 5.2 - Trigonometric Function of Real Numbers

  9. Even-Odd Properties • Sine, cosecant, tangent, and cotangent are odd functions. • Cosine and secant are even functions. 5.2 - Trigonometric Function of Real Numbers

  10. Example – pg. 384 • Find the exact value of the trigonometric functions at the given real number. 5.2 - Trigonometric Function of Real Numbers

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

  12. Examples – pg. 385 • Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant. 5.2 - Trigonometric Function of Real Numbers

  13. Examples – pg. 385 • Find the values of the trigonometric functions of t from the given information. 5.2 - Trigonometric Function of Real Numbers

  14. Examples – pg. 384 • Find the exact value of the trigonometric functions at the given real number. 5.2 - Trigonometric Function of Real Numbers

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