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Trigonometric Ratios

Trigonometric Ratios. Trigonometric Ratios. Used to find missing side lengths or angles of right triangles Compares the lengths of two sides of a right triangle Terminology: Sine (sin) Cosine (cos) Tangent (tan). Given Right Triangle ABC. B. c. a. A. C. b. Given A

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Trigonometric Ratios

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  1. Trigonometric Ratios

  2. Trigonometric Ratios • Used to find missing side lengths or angles of right triangles • Compares the lengths of two sides of a right triangle • Terminology: • Sine (sin) • Cosine (cos) • Tangent (tan)

  3. Given Right Triangle ABC B c a A C b • 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

  4. Trigonometric Ratios • Sin = Opposite =Opp Hypotenuse Hyp • Cos = Adjacent = Adj HypotenuseHyp • Tan = Opposite = Opp AdjacentAdj • S =O • H • C =A • H • T =O • A • SOH-CAH-TOA

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

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

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

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

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

  10. SOH-CAH-TOA Given Right Triangle ABCSolve for y A Hyp 27o y Adj 3 B x C

  11. SOH-CAH-TOA Given Right Triangle ABCSolve for x C Adj Opp x 12 58o B A

  12. THE END!!!! GO FORTH AND SOLVE……

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