Geom9point5and 6

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Geom9point5and 6

  1. 1. Trig Basics & Beyond
  2. 2. Objectives <ul><li>Review of: </li></ul><ul><ul><li>Sin, Cos, Tan </li></ul></ul><ul><li>Learn </li></ul><ul><ul><li>Csc, Sec, Cot </li></ul></ul><ul><li>Learn inverse sin, cos, & tan </li></ul><ul><li>Understand how to solve a right triangle </li></ul>
  3. 3. Sine <ul><li>Sine of A is: </li></ul><ul><li>length of side opposite A a </li></ul><ul><li>Length of hypotenuse c </li></ul>c a b A B C =
  4. 4. Cosine <ul><li>Cosine of A is: </li></ul><ul><li>length of side adjacent to A b </li></ul><ul><li>Length of hypotenuse c </li></ul>c a b A B C =
  5. 5. Tangent <ul><li>Tangent of A is: </li></ul><ul><li>length of side opposite to A a </li></ul><ul><li>Length of side adjacent to A b </li></ul>c a b A B C =
  6. 6. Shortcuts to Remembering <ul><li>Sin = opposite/hypotenuse </li></ul><ul><li>Cos = adjacent/hypotenuse </li></ul><ul><li>Tan = opposite/adjacent </li></ul><ul><li>SOHCAHTOA </li></ul>
  7. 7. Practice SOHCAHTOA <ul><li>Sin = opposite/___________ </li></ul><ul><li>Cos = _________/hypotenuse </li></ul><ul><li>Tan = opposite/________ </li></ul>
  8. 8. Practice – & reduce fractions <ul><li>Sin A </li></ul><ul><li>3/5 </li></ul><ul><li>Cos A </li></ul><ul><li>4/5 </li></ul><ul><li>Tan A </li></ul><ul><li>¾ </li></ul><ul><li>Cos B </li></ul><ul><li>3/5 </li></ul><ul><li>Sin B </li></ul><ul><li>4/5 </li></ul><ul><li>Tan B </li></ul><ul><li>4/3 </li></ul>35 21 28 A B C SOHCAHTOA
  9. 9. Practice – & reduce fractions <ul><li>Sin B </li></ul><ul><li>12/13 </li></ul><ul><li>Tan B </li></ul><ul><li>12/5 </li></ul><ul><li>Cos A </li></ul><ul><li>12/13 </li></ul><ul><li>Cos B </li></ul><ul><li>5/13 </li></ul><ul><li>Sin A </li></ul><ul><li>5/13 </li></ul><ul><li>Tan A </li></ul><ul><li>5/12 </li></ul>52 20 48 A B C SOHCAHTOA
  10. 10. Useful Stuff – Find a and b <ul><li>Sin A = opposite/hypotenuse </li></ul><ul><li>= a/24 </li></ul><ul><li>Sin 52 ◦ = a/24 </li></ul><ul><li>.7880 = a/24 </li></ul><ul><li>24*.7880 = 24*a/24 </li></ul><ul><li>a = 18.912 </li></ul>24 a b 52 ◦ B C SOHCAHTOA
  11. 11. Solving Triangles – Find a and b <ul><li>Cos A = adjacent/hypotenuse </li></ul><ul><li>= a/24 </li></ul><ul><li>cos 52 ◦ = b/24 </li></ul><ul><li>.6157 = b/24 </li></ul><ul><li>24*.6157 = 24*b/24 </li></ul><ul><li>b = 14.7768 </li></ul>24 a b 52 ◦ B C SOHCAHTOA
  12. 12. Inverse Sine <ul><li>If we know that the sine of angle A is .6691, then what is Angle A? </li></ul><ul><li>We call this concept “inverse sine” </li></ul><ul><li>It is written: sin -1 .6691 </li></ul><ul><li>How do you do this on your calculator? </li></ul>24 a b 52 ◦ B C
  13. 13. Solving Triangles – finding angles <ul><li>Sin A = opposite/hypotenuse </li></ul><ul><li>Sin A = 5/12 </li></ul><ul><li>Sin A = .4167 </li></ul><ul><li>A = 25 degrees </li></ul>12 5 b A B C SOHCAHTOA
  14. 14. Finding angles <ul><li>A + B + C = 180 degrees </li></ul><ul><li>25 + B + 90 = 180 </li></ul><ul><li>B = 65 degrees </li></ul>12 5 b A B C SOHCAHTOA
  15. 15. Another example – Find A, B, and x <ul><li>Tan A = opp/adj = 6/4 = 1.5 </li></ul><ul><li>Tan 56 = 1.4826, tan 57 = 1.5399, so 56 degrees is closest to A </li></ul><ul><li>B = 90 – A = 90 – 56 = 34 degrees </li></ul><ul><li>X 2 = 4 2 + 6 2 </li></ul><ul><li>X 2 = 52 </li></ul><ul><li>X = 7.211 </li></ul>x 4 6 A B C SOHCAHTOA
  16. 16. Solving Triangles <ul><li>When the question asks you to “solve the triangle”, it means find all unknown sides and angles. </li></ul><ul><li>For now, we are only solving RIGHT triangles. We’ll leave solving other triangles as something for you to look forward to . . . </li></ul>
  17. 17. What is a reciprocal? <ul><li>Two quantities are a pair of reciprocals if their product is +1 </li></ul><ul><li>8 and 1/8 are a pair of reciprocals </li></ul><ul><li>What is the reciprocal of 3/2? </li></ul>
  18. 18. Definitions of Cosecant, Secant, and Cotangent <ul><li>Sine is a reciprocal of cosecant </li></ul><ul><li>Sine = opp/hyp </li></ul><ul><li>Cosecant = Csc = hyp/opp </li></ul><ul><li>Cosine is a reciprocal of secant </li></ul><ul><li>Secant = sec = 1/cos = hyp/adj </li></ul><ul><li>Tangent is a reciprocal of cotangent </li></ul><ul><li>Cotangent = cot = adj/opp </li></ul>
  19. 19. <ul><li>csc A </li></ul><ul><li>5/3 </li></ul><ul><li>sec A </li></ul><ul><li>5/4 </li></ul><ul><li>cot A </li></ul><ul><li>4/3 </li></ul><ul><li>sec B </li></ul><ul><li>5/3 </li></ul><ul><li>cot B </li></ul><ul><li>3/4 </li></ul><ul><li>csc B </li></ul><ul><li>5/4 </li></ul>Practice – & reduce fractions 35 21 28 A B C
  20. 20. Homework <ul><li>Worksheets </li></ul>

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