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8.3 and 8.4 Trigonometric Ratios

8.3 and 8.4 Trigonometric Ratios. 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.

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8.3 and 8.4 Trigonometric Ratios

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  1. 8.3 and 8.4 Trigonometric Ratios

  2. 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

  3. Let ∆ABC be a right triangle. If you are standing from angle A, the following sides are labeled:opposite, adjacent and hypotenuse Trigonometric Ratios adjacent b cos A = = hypotenuse c opposite a sin A = = hypotenuse c opposite a tan A = = adjacent b

  4. If you were standing at angle B, you would have to re-label the sides ofopposite, adjacent and hypotenuse B Side hypotenuse c adjacent a angle B A b C side opposite to angle B Trigonometric Ratios adjacent a cos B = = hypotenuse c opposite b sin B = = hypotenuse c opposite b Tan B = = adjacent a

  5. The famous Indian… SOHCAHTOA Sin Cos Tan

  6. R 13 5 12 T S Ex. 1: Find sin, cos and tan of angle S opposite sin S = hypotenuse adjacent cosS = hypotenuse opposite tanS = adjacent

  7. R 13 5 12 T S Ex.2: Find the sin, cos and tan of angle R opposite sin R = hypotenuse adjacent cosR= hypotenuse opposite tanR = adjacent

  8. Using the Inverse • You can use the sin, cos and tan ratio and calculate it’s inverse, sin-1, cos-1, tan-1to find the measure of the angle. • Make sure your calculator is in degree mode!!! *make note: sin, cos, and tan are ratios. Inverses find angles!!!

  9. R 13 5 12 T S Let’s find angle S. opposite sin S = hypotenuse adjacent cosS = hypotenuse opposite tanS = adjacent

  10. R 13 5 12 T S Now let’s find the angle measure from a previous example opposite sin R = hypotenuse adjacent cosR= hypotenuse opposite tanR = adjacent

  11. Examples: Given the triangles below, find the missing angle measure to the nearest degree 6 2 6 8 ? ? 10

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