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7.4 trigonometry -_sol_g7

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Geometry-trig-Standard G.7--

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7.4 trigonometry -_sol_g7

1. 1. 7.4 Trigonometry <ul><li>SOL: G7 </li></ul><ul><li>Find trigonometric ratios using right Triangles </li></ul><ul><li>Solve problems using trigonometric ratios </li></ul>
2. 2. Trigonometric Ratios <ul><li>SOH CAH TOA </li></ul>= Opposite Hypotenuse <ul><li>Sine </li></ul>= Adjacent Hypotenuse <ul><li>Cosine </li></ul>= Opposite Adjacent <ul><li>Tangent </li></ul>
3. 3. Sine AB AB Opposite Hypotenuse Sin A = BC = AC = Opposite Hypotenuse Sin B =
4. 4. Cosine AB AB Adjacent Hypotenuse <ul><li>Cos A = </li></ul>Adjacent Hypotenuse <ul><li>Cos B = </li></ul>BC = AC =
5. 5. Tangent AC BC Opposite Adjacent <ul><li>Tan B = </li></ul>AC = Opposite Adjacent <ul><li>Tan A = </li></ul>BC =
6. 6. Example 1: <ul><li>Find sin L , cos L , tan L , sin N , Cos N , and tan N . Express each ratio as a fraction and as a decimal. </li></ul>Opp 8 17 15 = 0.47 Hyp 8 17 Adj = 0.88 Hyp 15 17 Opp = 0.53 Adj 8 15 Sin L = = Cos L = = Tan L = = Hypotenuse
7. 7. Example 1: continued <ul><li>Now lets do Sin N , Cos N , and Tan N . Express each ratio as a fraction and as a decimal. </li></ul>Opp 8 17 15 = 0.88 Hyp 15 17 Adj = 0.47 Hyp 8 17 Opp = 1.88 Adj 15 8 Sin N = = Cos N = = Tan N = = Hypotenuse
8. 8. Example 2: <ul><li>Find each value to the nearest ten thousandths. </li></ul><ul><li>a.) tan 56  = </li></ul><ul><li>b.) cos 89  = </li></ul>Make sure your calculator is in degree mode 1.4826 0.0175
9. 9. Example 3: <ul><li>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? </li></ul>opp 5 (sin 7  ) = y Convert to inches y = 12(0.6093467) 0.6093467 ft = y ≈ 7.3 hyp sin 7  = 5 (sin 7  ) = (5) y 5 Hypotenuse Opposite y 5 =
10. 10. Using Trigonometry to Find and Angle Measure <ul><li>We can also find an angle measure. </li></ul>If sin B = 0.7823, then sin -1 (0.7823) = B This is done in the calculator: Press the 2 nd key, press the sin (sin -1 ) key Type in 0.7823 and press enter B = 51.47 
11. 11. Examples 4: <ul><li>Find the measure of each acute angle to the nearest tenth degree. </li></ul><ul><li>a.) tan A = 0.2356, </li></ul><ul><li> </li></ul><ul><li>b.) cos R = 0.6401, </li></ul>A = 13.3 tan -1 (0.2356) = A cos -1 (0.6401) = R R = 50.2