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Trigonometric Ratios

Trigonometric Ratios. Geometry CP (Holt 8-2) K. Santos. Parts of a right triangle for Trig. A adjacent use < A as reference angle hypotenuse B C opposite Hypotenuse —always opposite the right angle

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Trigonometric Ratios

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  1. Trigonometric Ratios Geometry CP (Holt 8-2) K. Santos

  2. Parts of a right triangle for Trig. A adjacent use < A as reference angle hypotenuse B C opposite Hypotenuse—always opposite the right angle Opposite Side—side opposite the reference angle if the reference angle is < A then it is Adjacent Side—side touching the angle (not hypotenuse side) if the reference angle is < A then it is

  3. Identifying Parts in Right Triangle A B C Using <A Using <C Hypotenuse: Opposite Side: Adjacent Side:

  4. Trigonometric Ratios: SOH-CAH-TOA Sine ϑ = = SOH Cosine ϑ = =CAH Tangent ϑ = =TOA

  5. Example—Finding Ratios X Find the ratios. 10 8 Z 6 Y tan X = ??? tan X = tan X = = = .75 cos Z = ???? cos Z = cos Z = = = .6

  6. What does it mean???? In the last problem there was a solution: tan X = In your calculator there is a chart = .75 If you look-up .75 in the chart—tangent column it most closely matches 37 which is m < X Every ratio corresponds to a decimal which corresponds to the reference angle

  7. Calculator Mode: Calculators must be set on “degree” mode to access the chart for right triangle trigonometry. Do not want to be in “radian” mode—circle trigonometry. MODE---DEGREE Please check your mode every time you use a calculator We will round our decimals to two decimal places (hundredths)

  8. Calculator—find trig. ratio Use your calculator to ding each trigonometric ratio. Round your answer to the nearest hundredths. • cos (76 cos76 = 0.24 2. sin (8 sin 8 = 0.14 3. Tan (82) Tan 82

  9. Example—Finding a side x12 23 Always label your sides!!!!!! cosϑ= cos 23 = x = 12cos 23 x = 11.05

  10. Example—Finding a side 71 x 10 sin = sin 71= x sin 71 = 10 x = x = 10.58

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