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三角比equation問題,唔該...

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要solving equation by algebraic methods,,, 1) 2an3x=-4 2) (開方3) tan9x+30度0=2 3) 2sin(x-45度)=-1 ans: 1)38.9度,98.9度,158.9度,218.9度,278.9度,338.9度 2)19.1度 or 199.1度 3)25.5度,244.5度 求計法 唔該幫幫手~

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1) 2 tan3x= -4 Let k = 3x 2 tan k = - 4 tan k = -4/2 = -2 因為負數, 在 quadrant 2 and 4 k = (180o – 63.43o) = 116.56o or k = (360o - 63.43o) = 296.57o 3x = 116.56o or 3x = 296.57o x = 116.56o/3 = 38.9o or x = 296.57o/3 = 98.9o 你無指定 range, 假定 0o <= x <= 360o k = 116.56o + 360o = 476.56o, x =476.56o/3 = 158.9o k = 116.56o+ 720o = 836.56o, x = 836.56o/3 = 278.9o k = 296.57o + 360o = 656.57o, x =656.57o/3 = 218.9o k = 296.57o + 720o = 1016.57o, x =1016.57o/3 = 338.9o x = 38.9o,98.9o,158.9o,218.9o,278.9o,338.9o 2) (開方3) tan9x+30度0=2 .... ?? 請重寫的問題。如果有必要,使用括弧(bracket) 3) 2sin(x-45度)=-1 Let k = x - 45o 2sin k = -1 sin k = -0.5 k = 180o + 30o = 210 o or k = - 30o 210o = x - 45o, x = 210o + 45o = 255o -30o = x - 45o, x = 45o - 30o = 15o x = 15o or x = 255o Your given answers for question 3 are not right. Check: 2sin(15o- 45o) = -1 2sin(- 30o) = -1 2(-0.5)= -1 -1 = -1 2sin(255o- 45o) = -1 2sin(210o) = -1 2(-0.5) = -1 -1 = -1

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