Ex 2.2 answer.pdf

2 Trigonometric Ratios andApplications of Trigonometry (I)2.2 SineExtra Class Activity 1Find the values of sin α and sin β in the following. (The first one has been done as an example.) EN – SFNK OK = PKcbefpqsin α = b csin β = a cadepsin α =fsin α = rdqsin β =fsin β = _______ rrQK RK = SKnikmx 3 yjmisin α =lsin α = ksin α =njsin β =lsin β = ksin β =3x3yExtra Class Activity 2Use a calculator to find the values of the following. (Give the answers correct to 4 decimal places ifnecessary.) EN – QFNK E~F sin 20° = 0.342 0 EÄF sin 10° =0.173 60.866 0OK E~F sin 60° = EÄF sin 30° =0.965 9PK E~F sin 75° = EÄF sin 37.5° =0.707 1QK E~F sin 45° = EÄF sin 22.5° =0.50.608 80.382 7

10 Chapter 2 Trigonometric Ratios and Applications of Trigonometry (I)RKComplete the following table by using the results of questions N to Q. (Give the answers correctto 4 decimal places if necessary.)θ 10° 22.5° 30° 37.5°2θ 20° 45° 60° 75°2 × sin θsin 2θ0.347 2 0.765 4 1 1.217 60.342 0 0.707 1 0.866 0 0.965 9sin 2θ ≠ 2 sin θUse a calculator to find the values of the following. (Give the answers correct to 2 decimal places.)ES – TFSK E~F If sin α = 0.411 1, then α = 24.27° .EÄF If sin β = 0.822 2, then β = 55.31° .TK E~F If sin α = 0.333 3, then α = 19.47° .EÄF If sin β = 0.666 6, then β = 41.81° .From the results of questions S and T, we can see thatsin β = 2 sin α,but β ≠ 2α.Extra Example 1Use a calculator to find the values of the following.(Give the answers correct to 4 decimal places.)E~F sin 25°EÄF sin 34.21°EÅF sin 43°38′EÇF sin 28°57′26′′SolutionHave a TryUse a calculator to find the values of the following.(Give the answers correct to 4 decimal places.)E~F sin 38° = 0.615 7EÄF sin 54.39° = 0.813 0EÅF sin 73°28′ = 0.958 7EÇF sin 27°56′48′′ = 0.468 6E~FpíÉéhÉóëaáëéä~óEÄFpíÉéhÉóëaáëéä~ó125 25134.21 34.212sin0.42261...2sin0.56221...sin 25° = 0.422 6sin 34.21° = 0.562 2

2.2 Sine11EÅFpíÉéhÉóëaáëéä~óEÇFpíÉéhÉóëaáëéä~ó143 43128 282° , ”432° , ”28338 38357 574° , ”43.63333...4° , ”28.955sin0.690040...52626sin 43°38′ = 0.690 06° , ”28.95722...7sin0.48415...sin 28°57′26′′ = 0.484 2Extra Example 2Use a calculator to find the values of the following.E~F If sin θ = 0.275 9, find θ.(Give the answer correct to the nearest degree.)EÄF If sin θ = 0.785 1, find θ.(Give the answer correct to 2 decimal places.)EÅF If sin θ = 0.592 7, find θ.(Give the answer correct to the nearest minute.)EÇF If sin θ = 0.475 1, find θ.(Give the answer correct to the nearest second.)Have a TryUse a calculator to find the values of the following.E~F If sin θ = 0.752 3, then θ = 49°(Give the answer correct to the nearest degree.)EÄF If sin θ = 0.193 6, then θ =(Give the answer correct to 2 decimal places.)EÅF If sin θ = 0.857 2, then θ =(Give the answer correct to the nearest minute.)EÇF If sin θ = 0.327 1, then θ =11.16°59°0′19°5′34′′(Give the answer correct to the nearest second.)SolutionE~FpíÉéhÉóëaáëéä~óEÄFpíÉéhÉóëaáëéä~ó10.2759 0.275910.7851 0.78512INV0.27592INV0.78513 sin 16.01565...If sin θ = 0.275 9,then θ = 16°3 sin 51.72992...If sin θ = 0.785 1,then θ = 51.73°

12 Chapter 2 Trigonometric Ratios and Applications of Trigonometry (I)EÅFpíÉéhÉóëaáëéä~óEÇFpíÉéhÉóëaáëéä~ó10.5927 0.592710.4751 0.47512INV0.59272INV0.47513sin36.34884...3sin28.36586...4INV36.34884...4INV28.36586...5° , ”36°20′55.845° , ”28°21′57.10If sin θ = 0.592 7,then θ = 36°21′55.84′′ is roundedoff to 1′.If sin θ = 0.475 1,then θ = 28°21′57′′Extra Example 3Find θ in the figure.(Give the answer correct to the nearest minute.)Have a TryFind θ in the figure.(Give the answer correct to the nearest degree.)615157Solution6sin θ =15θ = 23°35′Solution7Q sin θ =15∴ θ = 28°Extra Example 4Find BC in the figure.(Give the answer correct to 1 decimal place.)Have a TryFind AC in the figure.(Give the answer correct to 1 decimal place.)CA33 B52A3252BC

2.2 Sine13SolutionBC= sin 32°ABBC = AB sin 32°= 52 × sin 32°= 27.6SolutionACQ = sin 52°AB∴ AC = AB · sin 52°= 33 × sin 52°= 26.0Extra Example 5Find AB and BC in the figure below.(Give the answers correct to 2 decimal places.)SolutionB25 20’C3AHave a TryFind AB and AC in the figure below.(Give the answers correct to 2 decimal places.)C1246 24’ABSolutionAC= sin 25°20′ABACAB =sin 25° 20'3=sin 25° 20′= 7.01In ∆ABC,AB 2 = AC 2 + BC 2BC 2 = AB 2 – AC 2= 7.011 2 – 3 2= 40.154BC = 6.34(Pyth. Theorem)BCQ= sin 46°24′ABBC∴ AB =sin 46° 24′12=sin 46° 24′In ∆ABC,= 16.57AB 2 = AC 2 + BC 2AC 2 = AB 2 – BC 2= 16.571 2 – 12 2= 130.587∴ AC = 11.43(Pyth. Theorem)

14 Chapter 2 Trigonometric Ratios and Applications of Trigonometry (I)Extra Exercise 2.2Level OneUse a calculator to find the values of the following. (Give the answers correct to 4 decimal places.) EN – PF=NKE~F sin 55° 0.819 2EÄF sin 78° 0.978 1EÅF sin 63° 0.891 0EÇF sin 18° 0.309 0=OKE~F sin 29.5° 0.492 4EÄF sin 33.82°EÅF sin 77.71° 0.977 1EÇF sin 52.87°0.556 60.797 3=PKE~F sin 36°29′ 0.594 6EÄF sin 45°2′30′′EÅF sin 65°58′27′′ 0.913 4EÇF sin 82°17′48′′0.707 60.991 0=QKUse a calculator to find θ in the following. (Give the answers correct to the nearest degree.)E~F sin θ = 0.375 2 θ = 22°EÄF sin θ = 0.125 7 θ = 7°EÅF sin θ = 2 3θ = 24°EÇF sin θ = θ = 35°53=RKUse a calculator to find θ in the following. (Give the answers correct to the nearest minute.)E~F sin θ = 0.982 4 θ = 79°14′ EÄF sin θ = 0.003 4 θ = 0°12′EÅF sin θ = 3 θ = 36°52′5EÇF sin θ = θ = 26°34′55Find the unknown angles in the following. (Give the answers correct to the nearest degree.) ES – UF=SK a = 23° =TK b = 35°=UK c = 64°57b20ca13418

2.2 Sine15Find the unknown angles in the following. (Give the answers correct to the nearest minute.) EV – NNF= VK p = 19°28′ NMK q = 36°52′ NNK 13r = 31°20′pq12610254rFind the unknowns in the following. (Give the answers correct to 2 decimal places.) ENO – NTFNOK a = 71.93NPK b = 7.08NQKc = 161.654610023 10’18b38 13’ca100NRK d = 26.92NSK e = 31.41NTKed68 15’35 67 25’2563 50’ff = 62.8258Level TwoNUK Find the values of the following. (Give the answers correct to 3 decimal places.)E~F sin 23° + 3 sin 32° EÄF 2 sin 24°13′ – sin 52°5′ 0.031EÅF1.980sin 18°42'sin 62° × sin 18°32′ – sin 68°19′ EÇF– 0.649sin 81°24'+ sin 72°35'1.278EÉF (sin 28°) 2 + (sin 62°) 2 EÑF (sin 57°) 2 + (sin 73°28′) 2 1.6221.000

16 Chapter 2 Trigonometric Ratios and Applications of Trigonometry (I)NVK Find θ in the following. (Give the answers correct to the nearest degree.)E~F sin θ = 2 3sin 28° 16' EÄF sin θ = 1 +θ = 18° 2 θ = 29°5OMK Find θ in the following. (Give the answers correct to 1 decimal place.)E~F sin θ = 1 2sin 45°+ sin 30°sin 40° θ = 18.7° EÄF sin θ = θ = 14.0°5ONK Find θ in the following. (Give the answers correct to the nearest minute.)E~F sin θ =θ = 59°35′221sin 60°+ sin 90° EÄF sin (θ – 20°) =4OOK Without using a calculator, determine whether the result is positive or negative in each of the following.E~F sin 50°25′ – sin 25°50′ Positive EÄF sin 72° – sin 37°20′ PositiveOPK Given that sin α = 0.819 2 and sin β = 0.756 3, where α and β are acute angles, which of the following iscorrect? Correct answer: (III) α > βEfF α < β EffF α = β EfffF α > β23θ = 48°8′Find the values of sin θ in the following. (Express the answers in fractions.) EOQ – OSFOQK 2ORK 40OSK 1524117168 2821852 2 38 2805 2 3Find the unknowns in the following. (Give the answers correct to 2 decimal places.) EOT – OVFOTK x = 9.77 OUK y = 21.12 and z = 25.46 OVK h = 16.26 and w = 18.7888xy18z23 hw135558 27’ 454560