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Chapter 4

Chapter 4. 4-4 Trigonometric functions at any angle. Objectives. Students will know how to evaluate trigonometric functions of any angle , Find reference angles Evaluate trigonometric functions of real numbers. Definition. Quadrants of circle. Example#1.

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Chapter 4

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  1. Chapter 4 4-4 Trigonometric functions at any angle

  2. Objectives • Students will know how to • evaluate trigonometric functions of any angle, • Find reference angles • Evaluate trigonometric functions of real numbers

  3. Definition

  4. Quadrants of circle

  5. Example#1 • Name the quadrant in which lies if the cotangent is positive and the sine is negative.

  6. Example#2 • Let (-3,4) be a point on the terminal side of • Find sine, cosine, and tangent of

  7. Example 3 • The point (-4, 10) is on the terminal side of an angle in standard position. Determine the exact values of the 6 trig functions.

  8. Student guided practice • Do problems 11-12 in your book page 289

  9. Evaluating Trigonometric functions • Given sin=-2/3 and tan • Find cosine and cotangent

  10. Example • Given that cot =-4/3 and sin >0 • Find the six trigonometric functions

  11. Trigonometric functions of quadrant angles • Evaluate the cosine function and the cotangent function • at the following four quadrant angles • A)

  12. Student guided practice • Do problems 29,30,39 in your book pagw 287 and 288

  13. Reference angle

  14. Reference angle • reference angle: the acute angle formed by the terminal side of θ and the x-axis is called the reference angle

  15. Example • Find the reference angle for the following • A)

  16. Student guided practice • Do odd problems fro 47-51 page 290

  17. Homework • Do problems 13-17, 23,27,52 and 53 in your book page 289 and 290

  18. Closure • Today we learned about trigonometric functions at any angle • Next we are going to see Graphs of sine and cosine

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