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

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

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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 Sin L = 8 17 15 == 0.4706 Hyp 8 17 Adj Cos L === 0.8825 Hyp 15 17 Opp Tan L === 0.5333 Adj 8 15 Hypotenuse N M L

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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 Sin N = 8 17 15 == 0.8825 Hyp 15 17 Adj Cos N === 0.4706 Hyp 8 17 Opp Tan N === 1.875 Adj 15 8 Hypotenuse N M L

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Find the indicated trigonometric ratio as a fraction and as a decimal. If necessary, round to the nearest ten-thousandths. 1.) sin A2.) tan B 3.) cos A4.) cos B 5.) sin D6.) tan E 7.) cos E8.) cos D

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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

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Example 3: Find x. 24° 19 x 1.) 31° 2.) x 34 tan 24° = x 19 (tan 24°)19 =x 8.459345021 = x 8.4593 ≈ x cos 31° = x 34 (cos 31°)34 =x 29.14368822 = x 29.1437 ≈ x

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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 sin 7 = 5(sin 7 ) = (5) y5y5 5(sin 7 ) = y Convert to inches y = 12(0.6093467) Hypotenuse Opposite 0.6093467 ft = y y ≈ 7.3121 in y5y5 = hyp

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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 2 nd key, press the sin (sin -1 ) key Type in 0.7823 and press enter θ = 51.47

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

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

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

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

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

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