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nite Geometry Name___________________________________ Kuta Software - Infinite Geometry World 5-‐1 Trigonometric Ratios Name___________________________________ Name: Ratios Trigonometric Ratios Date________________ Period____ Date________________ Period____ A. Determine the ratio of sides B. Determine the ratio to 3 decimal places ach trigonometric ratio. the value of each trigonometric ratio to the nearest ten-thou Find the value of each trigonometric ratio. value of each Find Find the trigonometric ratio to the nearest ten-thousandth. 2) cos C 1) tan Z 2)11) coscos C Z 12) cos C 11) cos Z 12) cos C B A X A Y Y 35 12 21 34 Z 9 34 30 Z Y 28 C 12 15 B 16 A A 35 X A 50 C 14) tan A 50 Z A Z 14) tan A A C 20 21 30 40 40 29 C C 30 B A C 45 B 16 13) tan C 32 28 36 27 4) tan X 40 40 36 30 15 C 13) tan C 4) tan X 3) sin C 9 Z X B 21 32 B B C X B 21 X Y 24 Y 24 15) tan C 16) tan X 15) tan C 6) sin A 5) cos A A 37 30 A B 12 32 C A B B 6 C C 12 35 16 40 A 8) sin C X A 8)17) C Z Y sinsin B Z 40 12 48 14 32 18) sin Z 35 Z B 37 50 35 Z C Y 30 48 12 A 50 X X 14 A Z 50 C 24 35 17) sin Z 7) sin Z 30 37 B B 40 40 C 40 32 X 24 34 16) tan X Y 6) sin A 50 37 Z 18) sin Z X 40 Y C 30 X Y 24 19) sin 48° 10) tan C 21) cos 61° 9) cos Z Y 20) sin 38° 19)tan sinC48° 10) C Z 24 20) sin 38° 22) cos 51° C 21) cos 61° Critical thinking questions: 45 30 18 Y X 36 36 22) cos 51° 45 23) Can the sine of an angle ever equal 2? 1 24) sin x = Critical thinking questions: Why or why not? A 3 A B 27 B 27 Find cos 23) Can the sine of an angle ever equal 2?x. X Why or why not? -1- eHdf3.2T B0o g YMOa7 waHin2 txSkh0oe uIQfmtn bnCfQit ©v 192T diKsehu5 hDtF wqnaoErionteAeV i wLu0GLGeOoJ dCY.Jm9 JWe1 A9tlavrlpqy0rI.yi8 FgNh3txsw crtessre9rcvgeHdf.T g YMOa7dse5 hwHintkhe uIbnCfQitnEiotAeV 0GGeOoJmWe1tarqyI.8 -1- Worksheet by Kuta Software LLC ©B t2O0k1E2B 4KXumtaau nSKoKf3t0wbamrYeE aLeLNCK.Z Q 5AplclF 1rxilgUhotdsT orYe8sWe1rFvUePdl.u w CMlaAdUem Ewci2trhS PIznsf2iAnQijtMeL LGdeaokmfe9t3rhyp.d -2- 1 3 Find cos 24) sin x = Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Kuta Software - Infinite Geometry Name___________________________________ Name___________________________________ Inverse Trigonometric Ratios Date________________ Period____ World 5-‐1 Trigonometric Ratios Name: Inverse Trigonometric Ratios Date________________ Period____ Find each angle measure to the nearest degree. Find each angle measure to the nearest degree. C. the angle to the nearest 10th of a degree 2) sin A = 0.5150 1)Determine sin B = 0.4848 1) sin B = 0.4848 2) sin A = 0.5150 3) cos A = 0.7431 3) cos A = 0.7431 4) cos W = 0.6157 4) cos W = 0.6157 5) cos A = 0.5878 5) cos A = 0.5878 6) tan W = 19.0811 6) tan W = 19.0811 7) cos A = 0.4226 8) tan W = 0.5317 7) cos A = 0.4226 8) tan W = 0.5317 Determine the missing side length and angles using only trig ratios Find the measure of the indicated angle to the nearest degree. Find the measure of the indicated angle to the nearest degree. 9) 10) 9) 10) 9 27 ? ? 27 ? ? 38 9 21 21 38 11) 11) 12) 12) 14 ? 14 42 29 ? 40 42 29 40 ? ? 13) 13) 39 10 ?39 14) 14) ? ©v D2h051h20 mKMuQt2aR sSBogflt3wraKr5eN eLgLCCd.e Z vAilAlK irmiLgchvthsz mr7eXsIexrovJemds.S y pMPaAdkej jwGiHtqh4 uIEnzfWiWnHiit8ez 9GEe0oJmPeItMrwyJ.W 11 ? ©v D2h051h20 mKMuQt2aR sSBogflt3wraKr5eN eLgLCCd.e Z vAilAlK irmiLgchvthsz mr7eXsIexrovJemds.S y pMPaAdkej jwGiHtqh4 uIEnzfWiWnHiit8ez 9GEe0oJmPeItMrwyJ.W 27 ?27 10 -1-1- 11 Worksheet by Kuta Software LLC Worksheet by Kuta Software LLC World 5-‐1 Trigonometric Ratios Name: 15) 15) 16) 16) 12 12 15) ? 16) 24 24 12 ? ? 20 13 20 ? 13 ? 20 13 ? 24 17) 17) ? ?17) ? 6 18) 8 6 18) 18) 8 8 5 5 5 6 ? ? 4 4? 4 19) 19) 20) 20) 20) 14 19) 14 14 51 5151 ? ?? 48 ? 21) 21) 21) 7 22) 7 ? ? 24) ? ? 51 ? 24) 8568 68 56 70 24) ? ? 42 51 85 30 30 68 23) 51 ? ? 24 23) 23) 30 24 24 25 34 ?34 16 16 25 25 22) 34 22) 16 ? 7 68 68 68 85 8585 48 50 48 50 ? ? 50 56 85 Critical thinking questions: ? 56 70 42 25) Find an angle x where sin x = cos x. Critical thinking questions: Critical thinking questions: 25) Find an angle x where sin x = cos x. 25) Find an angle x where sin x = cos x. ©d W2x0T1v2r GK6uRtNaj NSRowfStHwua4rbeK 7LZLpC3.j b uAIlqlk SrHi8gbh7txsC orEeNsueorovWekde.N 5 WMvaqdIe3 hwsi6t4hk zIrnlfWilnaiPt4ex VG5eMojmMe8tJrRyi.F 70 42 26) Draw and label all three sides of a right triangle that has a 40° angle and a hypotenuse of 10 cm. 26) Draw and label all three sides of a right 26) Draw and label all three sides of a right triangle that has a 40° angle and a triangle that has a 40° angle and a hypotenuse of 10 cm. hypotenuse of 10 cm. -2- Worksheet by Kuta Software LLC