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Chapter 8-4 part 1 Trigonometry

Chapter 8-4 part 1 Trigonometry. This lesson has been modified from the original in the following ways: Use of a trig. Table replaces a calculator. Students need access to a trig. table.

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Chapter 8-4 part 1 Trigonometry

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  1. Chapter 8-4 part 1 Trigonometry This lesson has been modified from the original in the following ways: Use of a trig. Table replaces a calculator. Students need access to a trig. table. a) rationale: CST questions are based on table and calculators are not allowed. Cheap accessible calculators can be used for trig. Students better understand the process involved with inverse trig. functions 2. Illustrations have been enlarged. 3. SohCahToa replaces original introduction. Teachers should tell the story of the old chief and his midnight encounter with a coffee table.

  2. trigonometry • Find trigonometric ratios using right triangles. • trigonometric ratio • sine • cosine • tangent • Solve problems using trigonometric ratios. Standards 18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x))2 = 1. (Key) Standards 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. (Key) Lesson 4 MI/Vocab

  3. Trig Ratios • Compares the lengths of two sides of a right triangle • Sine (sin) • Cosine (cos) • Tangent (tan)

  4. B c a A C b Given Rt. Triangle ABC • Given A • Side a is the Opposite • Side b is the Adjacent • Side c is the Hypotenuse • Given B • Side a is the Adjacent • Side b is the Opposite • Side c is still the Hypotenuse

  5. Sin = = Cos = = Tan = = Trig Ratios Opposite Opp Hypotenuse Hyp Adjacent Adj Hypotenuse Hyp Opposite Opp Adjacent Adj SOH-CAH-TOA

  6. SOH-CAH-TOA B c a A C b Given Rt. Triangle ABC • Given B • Sin B = • Cos B = • Tan B = Given A • Sin A = • Cos A= • Tan A=

  7. SOH-CAH-TOA B 5 4 A C 3 Given Rt. Triangle ABC • Given B • Sin B = • Cos B = • Tan B = Given A • Sin A = • Cos A= • Tan A=

  8. A. B. C. D. A. Find sin A. • A • B • C • D Lesson 4 CYP1

  9. A. B. C. D. B. Find cos A. • A • B • C • D Lesson 4 CYP1

  10. A. B. C. D. C. Find tan A. • A • B • C • D Lesson 4 CYP1

  11. A. B. C. D. D. Find sin B. • A • B • C • D Lesson 4 CYP1

  12. A. B. C. D. E. Find cos B. • A • B • C • D Lesson 4 CYP1

  13. A. B. C. D. F. Find tan B. • A • B • C • D Lesson 4 CYP1

  14. Find the Sine Cosine and Tangent of Find the Sine Cosine and Tangent of Find the Sine Cosine and Tangent of Find the Sine Cosine and Tangent of Using a Trig. Table

  15. A. Use your trig. table to find sin 48° to the nearest ten thousandth. • A • B • C • D A. 0.6691 B. 1.1106 C. 0.7431 D. 0.7314 Lesson 4 CYP2

  16. B. Use your trig. table to find cos 85° to the nearest ten thousandth. • A • B • C • D A. 0.0872 B. 0.9962 C. 11.4301 D. 0.0698 Lesson 4 CYP2

  17. Finding Missing Side Lengths • Decide which Trig function to use based on the given angle measure the given side and the unknown side • Substitute the given information and the unknown variable into the function’s equation • Solve for the variable (cross-multiply if necessary) • Calculate

  18. SOH-CAH-TOA B 10 x A C y Given Rt. Triangle ABCSolve for x Hyp Opp 32o

  19. SOH-CAH-TOA B 10 x A C y Given Rt. Triangle ABCSolve for y Hyp 32o Adj

  20. SOH-CAH-TOA Given Rt. Triangle ABCSolve for x A 27o y Adj 3 B Opp x C

  21. SOH-CAH-TOA 1 Given Rt. Triangle ABCSolve for y A Hyp 27o y Adj 3 B x C

  22. SOH-CAH-TOA 1 Given Rt. Triangle ABCSolve for x C Adj Opp x 12 58o B A

  23. Homework Chapter 8-4 • Pg 460 1,2,14-17,29-37,44,46,47,48 • Bring Calculators from now on!!!

  24. The Amazing Legend of… Chief SohCahToa

  25. Chief SohCahToa • Once upon a time there was a wise old Native American Chief named Chief SohCahToa. • He was named that due to an chance encounter with his coffee table in the middle of the night. • He woke up hungry, got up and headed to the kitchen to get a snack. • He did not turn on the light and in the darkness, stubbed his big toe on his coffee table….

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