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8-2 8-2 Trigonometric TrigonometricRatios Ratios Warm Up Lesson Presentation Lesson Quiz Holt Geometry Holt Geometry 8-2 Trigonometric Ratios <C a b <B c b Holt Geometry 8-2 Trigonometric Ratios 7) Holt Geometry x = 7.25 8-2 Trigonometric Ratios Objectives Find the sine, cosine, and tangent of an acute angle. Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems. Holt Geometry 8-2 Trigonometric Ratios SOH-CAHopposite sin x = hypotenus TOA e opposite tan x = adjacent adjacent cos x = hypotenus e Holt Geometry 8-2 Trigonometric Ratios opposite Sin(x)=hypotenus e ALWAYS an ANGLE!!! Holt Geometry 8-2 Trigonometric Ratios Writing Math In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the sine of A is written as sin A. Holt Geometry 8-2 Trigonometric Ratios Example 1: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. sin J 60 sin J = 61 Holt Geometry 8-2 Trigonometric Ratios Example 2: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. cos J 11 cos J =61 Holt Geometry 8-2 Trigonometric Ratios Example 3: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. tan K 11 tan k = 60 Holt Geometry 8-2 Trigonometric Ratios Example 4 Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. cos A 24 cos A =25 Holt Geometry 8-2 Trigonometric Ratios Example 5: Write cos 30° as a fraction. Holt Geometry s√3 = √3 cos 30 2s 2 = √3 cos 30 2 = 8-2 Trigonometric Ratios Example 6 Use a special right triangle to write tan 45° as a fraction. Draw and label a 45º-45º-90º ∆. 45° s 45° s tan 45 = s =1 s Holt Geometry 8-2 Trigonometric Ratios Example 7 Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° Caution! Be sure your calculator is in degree mode, not radian mode. sin 52° 0.79 Holt Geometry 8-2 Trigonometric Ratios Example 8 Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. cos 19° cos 19° 0.95 Holt Geometry 8-2 Trigonometric Ratios hyp EXAMPLE 9 opp x adj The trigonometric functions are: sine, cosine, tangent, cotangent, secant, and cosecant. opp adj tan x = sin x = cos x = hyp hyp hyp hyp csc x = opp sec x = cot x = adj S OH C AH T OA Holt Geometry opp adj adj opp 8-2 Trigonometric Ratios 13 EXAMPLE 10 5 x 12 Find the following: sine, cosine, tangent, cotangent, secant, and cosecant. 12 sin x = 5 cos x = tan x = 13 13 13 13 csc x = sec x = cot x = 5 12 S OH C AH T OA Holt Geometry 5 12 12 5 8-2 Trigonometric Ratios EXAMPLE 11 5 4 Find the following: sine, cosine, tangent, cotangent, secant, and cosecant. 3 sin x = 4 cos x = tan x = 5 5 5 5 csc x = 4 sec x = cot x = 3 S OH C AH T OA Holt Geometry x 3 4 3 3 4 8-2 Trigonometric Ratios EXAMPLE 12 Opposite Adjacent sin x = csc x = 5 3 Holt Geometry 3 5 So… the hypotenuse = 5 cos x = 4 5 tan x = 3 4 sec x = 5 4 cot x = 4 3 8-2 Trigonometric Ratios Caution! Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator. Holt Geometry 8-2 Trigonometric Ratios Example 13 Find the length. Round to the nearest hundredth. opp BC BC 38.07 ft Holt Geometry adj 8-2 Trigonometric Ratios Example 14: Find the length. Round to the nearest hundredth. opp QR hyp 12.9(sin 63°) = QR 11.49 cm QR Holt Geometry 8-2 Trigonometric Ratios Example 15 Find the length. Round to the nearest hundredth. FD hyp adj FD 25.74 m Holt Geometry