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8.3 Trigonometry

8.3 Trigonometry. SOL: G8 Objectives: The Student Will … Find trigonometric ratios using right Triangles Solve problems using trigonometric ratios. Sine =. Cosine =. Tangent =. Trigonometric Ratios. SOH CAH TOA. Opposite. Hypotenuse. Adjacent. Hypotenuse. Opposite.

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8.3 Trigonometry

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  1. 8.3 Trigonometry SOL: G8 Objectives: The Student Will … Find trigonometric ratios using right Triangles Solve problems using trigonometric ratios

  2. Sine = • Cosine = • Tangent = Trigonometric Ratios • SOH CAH TOA Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent

  3. BC Opposite Hypotenuse = Sin A = Opposite Hypotenuse AC Sin B = = B A C Sine AB AB Hypotenuse

  4. Adjacent Hypotenuse AC • Cos A = = Adjacent Hypotenuse BC • Cos B = = B A C Cosine AB AB Hypotenuse

  5. Opposite Adjacent BC • Tan A = = Opposite Adjacent AC • Tan B = = B A C Tangent AC BC Hypotenuse

  6. Hypotenuse Sin L = Tan L = Cos L = = = = Example 1: Find sin L, cos L, tan L, sin N, Cos N, and tan N. Express each ratio as a fraction and as a decimal. Opp N 8 = 0.47 Hyp 17 17 8 Adj 15 = 0.88 Hyp 17 L M 15 Opp 8 = 0.53 Adj 15

  7. Hypotenuse Sin N = Tan N = Cos N = = = = Example 1: continued Now lets do Sin N, Cos N, and Tan N. Express each ratio as a fraction and as a decimal. Opp 15 N = 0.88 Hyp 17 17 8 Adj 8 = 0.47 Hyp 17 L M 15 Opp 15 = 1.88 Adj 8

  8. Study Guide pg 369 Find the indicated trigonometric ratio as a fraction and as a decimal. If necessary, round to the nearest ten-thousandths. 1.) sin A 2.) tan B 3.) cos A 4.) cos B 5.) sin D 6.) tan E 7.) cos E 8.) cos D

  9. Example 2: Find each value to the nearest ten thousandths. a.) tan 56 = b.) cos 89 = Make sure your calculator is in degree mode 1.4826 0.0175

  10. x 34 x 19 1.) x 24° 19 2.) 34 31° x Example 3: Find x. (tan 24°)19 = x tan 24° = 8.459345021 = x 8.46 = x (cos 31°)34 = x cos 31° = 29.14368822 = x 29.14 = x

  11. y 5 = sin 7 = Opposite Hypotenuse y 5 5(sin 7) = (5) Example 4: A fitness trainer sets the incline on a treadmill to 7. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? opp hyp 5(sin 7) = y 0.6093467ft =y Convert to inches y = 12(0.6093467) ≈ 7.3

  12. Using Trigonometry to Find the Angle Measure We can also find an angle measure. If sin B = 0.7823, then sin-1(0.7823) = B This is done in the calculator: Press the 2nd key, press the sin (sin-1) key Type in 0.7823 and press enter B = 51.47

  13. Examples 5: Find the measure of each acute angle to the nearest tenth degree. a.) tan A = 0.2356, b.) cos R = 0.6401, tan-1(0.2356) = A A = 13.3 cos-1(0.6401) = R R = 50.2

  14. 15 18 15 18 tan-1 ( ) = 18 15 x° Example 6: tan x° = Find x. x° 39.80557109° = x 39.81° =

  15. 12 17 17 17 17 17 (sin-1) = x 12 12 17 12 x° Example 7: sin x° = Find x. (sin x°)17 = 12 (sin x°)17 = 12 (sin x°) = 44.9° = 44.90087216° = x

  16. Study Guide pg 370 Find x. Round to the nearest tenth.

  17. Study Guide pg 370 Find x. Round to the nearest tenth.

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