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8.5 and 8.6 Trigonometric Ratios

8.5 and 8.6 Trigonometric Ratios. Agenda and Objectives. Agenda Finish quiz (review first before I give it back to you) Start notes/powerpoint on trig ratios Classwork Start homework Objective Find the sine, the cosine, and the tangent of an acute triangle. Finding Trig Ratios.

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8.5 and 8.6 Trigonometric Ratios

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  1. 8.5 and 8.6 Trigonometric Ratios

  2. Agenda and Objectives • Agenda • Finish quiz (review first before I give it back to you) • Start notes/powerpoint on trig ratios • Classwork • Start homework • Objective • Find the sine, the cosine, and the tangent of an acute triangle.

  3. Finding Trig Ratios • A trig ratio is a ratio of the lengths of two sides of a right triangle. • The word trigonometry is derived from the ancient Greek language and means measurement of triangles. • The three basic trig ratios are sine, cosine, and tangent. • Abbreviated as sin, cos, and tan respectively

  4. Let ∆ABC be a right triangle. The sin, the cos, and the tan of the acute angle A are defined as follows: Trigonometric Ratios Side adjacent to A b cos A = = hypotenuse c Side opposite A a sin A = = hypotenuse c Side opposite A a tan A = = Side adjacent to A b

  5. The famous Indian… SOHCAHTOA Sin Cos Tan

  6. Ex. 1: Find the sin, the cos, and the tan of the indicated angle. opposite 5 sin S = ≈ 0.3846 hypotenuse 13 adjacent cosS = 12 ≈ 0.9231 hypotenuse 13 opposite tanS = 5 ≈ 0.4167 adjacent 12

  7. Ex. 1: Find the sin, the cos, and the tan of the indicated angle. opposite 12 sin R = ≈ 0.9231 hypotenuse 13 adjacent cosR= 5 ≈ 0.3846 hypotenuse 13 opposite tanR = 12 ≈ 2.4 adjacent 5

  8. Ex. 2: Find the sin, the cos, and the tan of 45 opposite 1 √2 sin 45= = ≈ 0.7071 hypotenuse √2 2 adjacent 1 √2 cos 45= = ≈ 0.7071 hypotenuse √2 2 opposite 1 tan 45= adjacent = 1 1 You could begin by sketching the special triangle 45-45-90, but let’s open your book to page 311 and look it up! √2 45

  9. You try: Find the sin, the cos, and the tan of 30 opposite sin 30= hypotenuse adjacent cos 30= hypotenuse opposite tan 30= adjacent First try using the triangle at the right to figure out the measure. Then compare your answers to the table on page 311. 30 √3

  10. Ex: 5 Using a Calculator • You can use a calculator to approximate the sin, cos, and the tan of 74. Make sure that your calculator is in degree mode. • The following table shows some sample keystroke sequences accepted by most calculators.

  11. Sample keystrokes

  12. More examples

  13. Independent Practice • Page 306 1-7 • Page 313 1-7 • HOMEWORK • Page 308 2-18 even • page 314 2-12 even

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