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Trigonometric Ratios – Introduction

Trigonometric Ratios – Introduction. Geometry A BowerPoint Presentation. Right Triangle Ratios. ∆ ABC has three angles… ∡ C is a right angle ∡ A and ∡ B are acute angles We can make ratios related to the acute angles in ∆ ABC. A. 5. 3. 4. C. B. Choose an acute angle.

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Trigonometric Ratios – Introduction

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  1. Trigonometric Ratios – Introduction Geometry A BowerPoint Presentation

  2. Right Triangle Ratios • ∆ABC has three angles… • ∡C is a right angle • ∡A and ∡B are acute angles • We can make ratios related to the acute angles in ∆ABC A 5 3 4 C B

  3. Choose an acute angle • Let’s start with ∡A ! • We need to label the three sides of the triangle with their positions relative to ∡A . A 5 3 4 C B

  4. Label the hypotenuse (hyp) • Label the side that is the hypotenuse • This side is always across from the right angle A 5 3 4 C B

  5. Label the hypotenuse (hyp) • Label the side that is the hypotenuse • This side is always across from the right angle A 5 hyp 3 4 C B

  6. Label the opposite leg (opp) • Label the leg opposite from ∡A • This leg doesn’t touch ∡Aat all – it is across the triangle from ∡A . A 5 hyp 3 4 C B

  7. Label the opposite leg (opp) • Label the leg opposite from ∡A • This leg doesn’t touch ∡Aat all – it is across the triangle from ∡A . A 5 hyp 3 4 C B opp

  8. Label the adjacent leg (adj) • Label the leg adjacent to ∡A • This leg does touch ∡A - it helps to make ∡A . A 5 hyp 3 4 C B opp

  9. Label the adjacent leg (adj) • Label the leg adjacent to ∡A • This leg does touch ∡A - it helps to make ∡A . A 5 hyp adj 3 4 C B opp

  10. Tangent [tan θ] • The tangent (tan) ratio involves only the legs of the triangle. • We will use opp and adj A 5 hyp adj 3 4 C B opp

  11. Tangent [tan θ] opp tan θ = adj A 5 hyp adj 3 4 C B opp

  12. Tangent [tan θ] opp 4 tan A = = or 1.3333 adj 3 Our example Exact fraction Rounded to four decimal places A 5 hyp adj 3 4 C B opp

  13. Sine [sin θ] • The sine (sin) ratio involves the hypotenuse and one of the legs. • We will use opp and hyp A 5 hyp adj 3 4 C B opp

  14. Sine [sin θ] opp sin θ = hyp A 5 hyp adj 3 4 C B opp

  15. Sine [sin θ] opp 4 sin A = = or 0.8 hyp 5 Our example Exact fraction Decimal form A 5 hyp adj 3 4 C B opp

  16. Cosine [cosθ] • The cosine (cos) ratio also involves the hypotenuse and one of the legs. • We will use adj and hyp A 5 hyp adj 3 4 C B opp

  17. Cosine [cosθ] adj cos θ = hyp A 5 hyp adj 3 4 C B opp

  18. Cosine [cosθ] adj 3 cosA = = or 0.6 hyp 5 Our example Exact fraction Decimal form A 5 hyp adj 3 4 C B opp

  19. Hard to remember? • There’s a simple memory trick for these trigonometric ratios…

  20. SOH – CAH – TOA • sin θ = Opp / Hyp • cos θ = Adj / Hyp • tan θ = Opp / Adj

  21. Your turn! • Find sin X , cos X , and tan X • Remember to label hyp, opp, & adj • Find answers as both fractions and decimals (rounded to four places) Z 29 20 21 Y X

  22. BowerPower.net

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