8.5 and 8.6 Trigonometric Ratios

Agenda and Objectives Agenda Objective 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 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

Trigonometric Ratios Let ∆ABC be a right triangle. The sin, the cos, and the tan of the acute angle A are defined as follows: 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

The famous Indian… SOHCAHTOA Sin Cos Tan

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

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

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

You try: Find the sin, the cos, and the tan of 30 Triangle Book 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

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.

Sample keystrokes

More examples

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