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Chapter 4 Trigonometry Section 4 Trigonometric Functions of Any Angle

Chapter 4 Trigonometry Section 4 Trigonometric Functions of Any Angle. to infinity and beyond . . . ! Math Analysis. Objectives. Evaluate trigonometric functions of any angle to ± infinity Use reference angles to evaluate trigonometric functions.

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Chapter 4 Trigonometry Section 4 Trigonometric Functions of Any Angle

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  1. Chapter 4 TrigonometrySection 4 Trigonometric Functions of Any Angle to infinity and beyond . . . ! Math Analysis

  2. Objectives • Evaluate trigonometric functions of any angle to ± infinity • Use reference angles to evaluate trigonometric functions. • Use trig models to solve real world problems

  3. Definitions of trigonometric functions Review Syr Cxr Tyx

  4. Find the trig functions using a point on the terminal side syr cxr tyx • (-3, 4)

  5. Quadrant angles Review x y

  6. Trigonometric function signs Star All All 6 trig functions are positive in quadrant 1 Sin/csc Trig Class Tan/cot Cos/sec

  7. Find the quadrant • sinθ > 0; cosθ <0 • sinθ < 0; cosθ > 0

  8. Reference angle Let θ be an angle in standard position. Its reference angle is the acute angle θ‘ formed by the terminal side of θ and the horizontal axis.

  9. Reference angles are always measured between the x axis and the terminal side of the angle (always +!) • Notice the butterfly shape

  10. Drawing Reference Angles Find the reference angle θ', and sketch θ and θ' in standard position. 2) 1) θ = -145°

  11. Finding the Trig functions of any angle • Find the reference angle • Determine the value of the given trig function of the reference angle. • Determine the sign—based on the quadrant of the given (original) angle

  12. Now: Find all 6 trig functions of an angle Find the six trigonometric functions of θ with the given constraint.

  13. Now, let’s make it tougher The terminal side of θ lies on the line y = (1/3)x in quadrant I. Find the values of the 6 trig functions of θ by finding a point on the line. sin θ = cos θ = csc θ = sec θ = tan θ = cot θ =

  14. Try These: Find the values of the six trig functions of θ with the given constraints. sin θ = 0; where sec θ = -1 Find the reference angle θ‘ and sketch it and the angle θ in standard position. a) θ = 3.5 b) θ = 750°

  15. Find the trig functions of an angle Evaluate the sine, cosine, and tangent of the angle without using a calculator. -405°

  16. Do 88(a)&(c)

  17. Do 91

  18. Objectives • Evaluate trigonometric functions of any angle to ± infinity • Syr Cxr Tyx • Quadrantal Angles • Use reference angles to evaluate trigonometric functions. • Find ref < • Find trig value of ref < • Determine sign of trig value for given < • Use trig models to solve real world problems • Draw, identify, solve

  19. Homework Pg. 284: 3-52 (multiples of 3-- i.e. 3, 6, 9, etc.)

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