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# Trigonometry 1

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Introduction to sine, cosine and tangent

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### Trigonometry 1

1. 2. <ul><li>Explain the term trigonometry. </li></ul><ul><li>Identify the three trigonometric ratios that apply to right angle triangles. </li></ul><ul><li>Calculate values for the three trigonometric ratios that apply to right angled triangles. </li></ul>
2. 3. <ul><li>Deals with the measurements of the sides and angles of triangles and their relationships with each other. </li></ul><ul><li>For right angled triangles there are six trigonometric ratios that apply. </li></ul><ul><li>We use the following three ratios in the main. </li></ul>
3. 4. Sine Ɵ = opposite__ hypotenuse Cosine Ɵ = adjacent__ hypotenuse Tangent Ɵ = opposite adjacent
4. 5. <ul><li>SOHCAHTOA . </li></ul><ul><li>S ine Ɵ = O pposite___ SOH </li></ul><ul><li> H ypotenuse </li></ul><ul><li>C osine Ɵ = A djacent__ CAH </li></ul><ul><li> H ypotenuse </li></ul><ul><li>T angent Ɵ = O pposite_ TOA </li></ul><ul><li> A djacent </li></ul>
5. 6. <ul><li>Find the unknown angles in the following triangle. </li></ul>3m 5m 4m Ø
6. 7. <ul><li>Since we know the length of each side we can use any of the three ratios to find Ɵ and Ø. </li></ul><ul><li>Sin Ɵ = _ opposite__ = 3m = 0.6 </li></ul><ul><li> hypotenuse 5m </li></ul><ul><li>Cos Ɵ = _ adjacent__ = 4m = 0.8 </li></ul><ul><li> hypotenuse 5m </li></ul><ul><li>Tan Ɵ = opposite = 3m = 0.75 </li></ul><ul><li>adjacent 4m </li></ul>Ø 5m 4m 3m
7. 8. <ul><li>To find Ɵ you should use your calculator. </li></ul><ul><li>Sin Ɵ = opposite = 3m = 0.6 </li></ul><ul><li> hypotenuse 5m </li></ul><ul><li>Sin Ɵ = 0.6 </li></ul><ul><li>Ɵ = Sinˉ¹ 0.6 </li></ul><ul><li>Ɵ = 36.87° </li></ul>5m 4m 3m Ø
8. 9. <ul><li>Ø can be found from 180 - 90 - 36.87 = 53.13 ° </li></ul><ul><li>This can be proved by trigonometry . </li></ul><ul><li>Sin Ø = _ opposite__ = 4m = 0.8 Ø = 53.13 ° </li></ul><ul><li> hypotenuse 5m </li></ul><ul><li>Cos Ø = _ adjacent__ = 3m = 0.6 Ø = 53.13 ° </li></ul><ul><li> hypotenuse 5m </li></ul><ul><li>Tan Ø = opposite = 4m = 1.33 Ø = 53.13 ° </li></ul><ul><li>adjacent 3m </li></ul>
9. 10. 3m 5m 4m Ø Ɵ = 36.87° Ø = 53.13°
10. 11. <ul><li>Explain the term trigonometry. </li></ul><ul><li>Identify the three trigonometric ratios that apply to right angle triangles. </li></ul><ul><li>Calculate values for the three trigonometric ratios that apply to right angled triangles. </li></ul>