1 / 11

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.

rue
Télécharger la présentation

8.3 and 8.4 Trigonometric Ratios

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related