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Sec. 8 – 4 Sine and Cosine Ratios

Sec. 8 – 4 Sine and Cosine Ratios. Objectives: 1) To use sine and cosine to determine side lengths in Δ s. 2) To use the sin -1 and the cos -1 to solve for  measures. Just Buttons on the Calculator!. Sine and Cosine are ratios of sides in a Right Δ. Sin. Cos.

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Sec. 8 – 4 Sine and Cosine Ratios

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  1. Sec. 8 – 4Sine and Cosine Ratios Objectives: 1) To use sine and cosine to determine side lengths in Δs. 2) To use thesin-1 and the cos-1 to solve for  measures.

  2. Just Buttons on the Calculator! • Sine and Cosine are ratios of sides in a Right Δ. Sin Cos

  3. The Sine and Cosine ratio in Rt. Δs Oppisite Side Sin  = Hypotenuse Adjacent Side Cos  = Hypotenuse Hyp Opposite  Adjacent

  4. Write the Sin and Cos Ratio Sin T = Cos T = Sin G = Cos G = 8 Opp = What do we call G and T? Complementary 17 Hyp G 15 Adj = 17 Hyp Interesting 17 15 Opp 8 = 17 Hyp 8 Adj R = T 15 17 Hyp For complementary s: Sin X = Cos Y

  5. Ex.1: Solve for the missing variables. Lets solve for x first. Opp 6cm Sin 20 = Hyp x x Sin 20 = 20° 6 y (6)(.342) = x 2.1 = x Now solve for y. Adj Cos 20 = Hyp (6)(.939) = y 5.6 = y y Cos 20 = 6

  6. The Sin-1 Cos-1 and Tan-1 • Use it when you are looking for missing s. Use the shift (2nd) Key Sin-1 Cos-1 Sin Cos

  7. Find the missing s Any of the Trig ratios will work since you have all three sides. Use the inverse sine ratio to solve for x. y° 3.5 Sin x = 4.0 Sin-1 (.875) = x 61° = x Sin x = .875 4.0 Easier Way? Use the inverse cosine ratio to solve for y. 3.5 3.5 Cos y = 4.0 Cos-1 (.875) = y 29° = y x° Cos y = .875 1.9

  8. Pneumonic Device S O H C A HT O A = = = ine angent djacent pposite osine ypotenuse ypotenuse pposite djacent SOH CAH TOA

  9. How do you know what trig ratio to use? • It depends on what is given to you and where you are trying to go. 22° x x 15 40° 55 Cosine Tangent

  10. What have you learned?? • Sin  = • Cos  = • Tan  = Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent ** Use the Sin-1 and Cos-1 when looking for the  measures.

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