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4.1 Right Triangle Trigonometry Slide 2 Sin = opp hyp Slide 3 Sin = opp hyp Csc = hyp opp Slide 4 Sin = opp hyp Cos = adj hyp Csc = hyp opp Slide 5 Sin = opp hyp Cos = adj hyp Csc = hyp opp Sec = hyp adj Slide 6 Sin = opp hyp Cos = adj hyp Tan opp adj Csc = hyp opp Sec = hyp adj Slide 7 Sin = opp hyp Cos = adj hyp Tan opp adj Csc = hyp opp Sec = hyp adj Cot = adj opp Slide 8 Sin = opp hyp Cos = adj hyp Tan opp adj Csc = hyp opp Sec = hyp adj Cot = adj opp Csc = 1 sin Slide 9 Sin = opp hyp Cos = adj hyp Tan opp adj Csc = hyp opp Sec = hyp adj Cot = adj opp Csc = 1 sin Sec = 1 cos Slide 10 Sin = opp hyp Cos = adj hyp Tan opp adj Csc = hyp opp Sec = hyp adj Cot = adj opp Csc = 1 sin Sec = 1 cos Cot = 1 tan Slide 11 Ex. 1 Find the exact values of the six trigonometric functions of . 8 17 15 Slide 12 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp hyp 8 17 15 Slide 13 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 hyp 17 8 17 15 Slide 14 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp hyp 17 opp 8 17 15 Slide 15 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 8 17 15 Slide 16 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj hyp 8 17 15 Slide 17 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15 hyp 17 8 17 15 Slide 18 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15Sec = hyp hyp 17 adj 8 17 15 Slide 19 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15Sec = hyp = 17 hyp 17 adj 15 8 17 15 Slide 20 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15Sec = hyp = 17 hyp 17 adj 15 Tan = opp adj 8 17 15 Slide 21 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15Sec = hyp = 17 hyp 17 adj 15 Tan = opp = 8 adj 15 8 17 15 Slide 22 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15Sec = hyp = 17 hyp 17 adj 15 Tan = opp = 8 Cot = adj adj 15 opp 8 17 15 Slide 23 Ex. 1 Find the exact values of the six trigonometric functions of . Sin = opp = 8 Csc = hyp = 17 hyp 17 opp 8 Cos = adj = 15Sec = hyp = 17 hyp 17 adj 15 Tan = opp = 8 Cot = adj = 15 adj 15 opp 8 8 17 15 Slide 24 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Slide 25 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Slide 26 2 Slide 27 2 5 Slide 28 21 2 5 Slide 29 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Sin = opp hyp 21 2 5 Slide 30 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Sin = opp = 21 hyp 5 21 2 5 Slide 31 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Sin = opp = 21 hyp 5 Tan = opp adj 21 2 5 Slide 32 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Sin = opp = 21 hyp 5 Tan = opp = 21 adj 2 21 2 5 Slide 33 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp opp Sin = opp = 21 hyp 5 Tan = opp = 21 adj 2 21 2 5 Slide 34 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ opp 21 Sin = opp = 21 hyp 5 Tan = opp = 21 adj 2 21 2 5 Slide 35 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ = 521 opp 21 21 Sin = opp = 21 hyp 5 Tan = opp = 21 adj 2 21 2 5 Slide 36 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ = 521 opp 21 21 Sin = opp = 21 Sec = hyp hyp 5 adj Tan = opp = 21 adj 2 21 2 5 Slide 37 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ = 521 opp 21 21 Sin = opp = 21 Sec = hyp = 5 hyp 5 adj 2 Tan = opp = 21 adj 2 21 2 5 Slide 38 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ = 521 opp 21 21 Sin = opp = 21 Sec = hyp = 5 hyp 5 adj 2 Tan = opp = 21 Cot = adj adj 2 opp 21 2 5 Slide 39 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ = 521 opp 21 21 Sin = opp = 21 Sec = hyp = 5 hyp 5 adj 2 Tan = opp = 21 Cot = adj = 2_ adj 2 opp 21 21 2 5 Slide 40 Ex. 2 If Cos = 2 / 5, find the exact values of the five remaining trigonometric functions for . Csc = hyp = 5_ = 521 opp 21 21 Sin = opp = 21 Sec = hyp = 5 hyp 5 adj 2 Tan = opp = 21 Cot = adj = 2_ = 221 adj 2 opp 21 21 21 2 5 Slide 41 Ex. 3 Find the value of x. Round to the nearest tenth, if necessary. 42 18 x Slide 42 Ex. 3 Find the value of x. Round to the nearest tenth, if necessary. Cos = adj hyp 42 18 x Slide 43 Ex. 3 Find the value of x. Round to the nearest tenth, if necessary. Cos = adj hyp Cos 42 = x 18 42 18 x Slide 44 Ex. 3 Find the value of x. Round to the nearest tenth, if necessary. Cos = adj hyp Cos 42 = x 18 18Cos 42 = x 42 18 x Slide 45 Ex. 3 Find the value of x. Round to the nearest tenth, if necessary. Cos = adj hyp Cos 42 = x 18 18Cos 42 = x 13.4 x 42 18 x Slide 46 Ex. 4 Find the measure of angle . Round to the nearest degree, if necessary. 26 11 Slide 47 Ex. 4 Find the measure of angle . Round to the nearest degree, if necessary. Tan = opp adj 26 11 Slide 48 Ex. 4 Find the measure of angle . Round to the nearest degree, if necessary. Tan = opp adj Tan = 26 11 26 11 Slide 49 Ex. 4 Find the measure of angle . Round to the nearest degree, if necessary. Tan = opp adj Tan = 26 11 = tan -1 ( 26 / 11 ) 26 11 Slide 50 Ex. 4 Find the measure of angle . Round to the nearest degree, if necessary. Tan = opp adj Tan = 26 11 = tan -1 ( 26 / 11 ) 67 26 11 Slide 51 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. 35 x 10 z Y ZX Slide 52 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = opp adj 35 x 10 z Y ZX Slide 53 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = opp adj Tan 35 = x 10 35 x 10 z Y ZX Slide 54 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = opp adj Tan 35 = x 10 10Tan 35 = x 35 x 10 z Y ZX Slide 55 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = opp adj Tan 35 = x 10 10Tan 35 = x x 7.0 35 x 10 z Y ZX Slide 56 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = oppCos = adj adj hyp Tan 35 = x 10 10Tan 35 = x x 7.0 35 x 10 z Y ZX Slide 57 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = oppCos = adj adj hyp Tan 35 = x Cos 35 = 10 10 z 10Tan 35 = x x 7.0 35 x 10 z Y ZX Slide 58 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = oppCos = adj adj hyp Tan 35 = x Cos 35 = 10 10 z 10Tan 35 = xz = 10___ x 7.0 Cos 35 35 x 10 z Y ZX Slide 59 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = oppCos = adj adj hyp Tan 35 = x Cos 35 = 10 10 z 10Tan 35 = xz = 10___ 12.2 x 7.0 Cos 35 35 x 10 z Y ZX Slide 60 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = oppCos = adj35 + Y = 90 adj hyp Tan 35 = x Cos 35 = 10 10 z 10Tan 35 = xz = 10___ 12.2 x 7.0 Cos 35 35 x 10 z Y ZX Slide 61 Ex. 5 Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. Tan = oppCos = adj35 + Y = 90 adj hypY = 55 Tan 35 = x Cos 35 = 10 10 z 10Tan 35 = xz = 10___ 12.2 x 7.0 Cos 35 35 x 10 z Y ZX