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Trigonometry

Trigonometry. Objectives: The Student Will … Find trigonometric ratios using right Triangles Solve problems using trigonometric ratios. HOMEWORK: Sin, cos, tan Practice WS `. Sine =. Cosine =. Tangent =. Trigonometric Ratios. SOH CAH TOA. Opposite. Hypotenuse. Adjacent.

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Trigonometry

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  1. Trigonometry Objectives: The Student Will … Find trigonometric ratios using right Triangles Solve problems using trigonometric ratios HOMEWORK: Sin, cos, tan Practice WS `

  2. Sine = • Cosine = • Tangent = Trigonometric Ratios • SOH CAH TOA Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Standard decimal  side lengths  ten thousandths (4)  angle measures  hundredths (2)

  3. 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.(ten-thousandths) Opp N 8 = 0.4706 Hyp 17 17 8 Adj 15 = 0.8825 Hyp 17 L M 15 Opp 8 = 0.5333 Adj 15

  4. 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. (ten-thousandths) Opp 15 N = 0.8825 Hyp 17 17 8 Adj 8 = 0.4706 Hyp 17 L M 15 Opp 15 = 1.875 Adj 8

  5. 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

  6. 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

  7. 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 8.4593 ≈ x (cos 31°)34 = x cos 31° = 29.14368822 = x 29.1437 ≈ x

  8. 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) y≈ 7.3121 in

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

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

  11. 15 18 15 18 tan-1 ( ) = 18 15 x° Example 6: tan x° = Find x. x° 39.80557109° = x 39.81° ≈ x

  12. 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

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

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

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