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Understanding Odd and Even Functions in Trigonometry: Evaluating Trigonometric Functions

This guide explores the concepts of odd and even functions in trigonometry and demonstrates how to evaluate these functions using a calculator. Odd functions such as sine and tangent exhibit properties like sin(-θ) = -sin(θ), while even functions such as cosine and secant satisfy cos(-θ) = cos(θ). Through detailed examples, we will find trigonometric function values such as sin(θ), cos(θ), and their reciprocals. Additionally, using the SOHCAHTOA acronym, we will calculate values of the six trigonometric functions for various angles.

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Understanding Odd and Even Functions in Trigonometry: Evaluating Trigonometric Functions

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  1. Odds and Even functions Evaluating trig functions Use a calculator to evaluate trig functions 2.3 Right Triangle Trigonometry

  2. Odds and Even Functions • Odd Functions sin (-) = -sin  tan (- ) = -tan  csc (- ) = -csc  cot(- ) = -cot  • Even Functions cos (-) = cos  sec (- ) = sec 

  3. Example • If sin (-) = 3/5 Find sin () csc () • If cos () = -3/4 Find cos (-) sec (-) • If cos () = 4/5 Find cos (-) cos ( + )

  4. The Six Trigonometric Functions Hypotenuse B Opposite A Adjacent

  5. The Six Trigonometric Functions Hypotenuse B Adjacent A Opposite

  6. 6 Trigonometric Functions sin  = opp cos = adj tan = opp hyp hyp adj SOHCAHTOA AKA And their reciprocals!!! csc  = hyp sec  = hyp cot = adj opp adj opp

  7. Example Find the values of the six trigonometric functions of . 13 5 

  8. Example Find the values of the six trigonometric functions of . 4  4

  9. Example Find the values of the six trigonometric functions of . cos  = 5/7

  10. Example Find the values of the six trigonometric functions of . cot  = 5

  11. Example Find the values of the six trigonometric functions of . sec  = 6

  12. Example Find the values of the six trigonometric functions of . csc  =17/4

  13. Homework • PAGE 103 (31, 33, 35) • Page 113 (1-21 odd)

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