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受欢迎的三角函数 >

solvefor x,(d^2-3d+2)y=sin(e^x)

解答

求解

x, (d^{2} - 3 d + 2) y = sin (e^{x})

解答

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn), x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

求解步骤

(d^{2} - 3 d + 2) y = sin (e^{x})

交换两边

sin (e^{x}) = (d^{2} - 3 d + 2) y

使用反三角函数性质

sin (e^{x}) = (d^{2} - 3 d + 2) y

sin (e^{x}) = (d^{2} - 3 d + 2) y

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn, e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn, e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

解

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn : x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn

使用指数运算法则

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn

若

f (x) = g (x)

，则

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

使用对数计算法则:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

解

e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn : x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

使用指数运算法则

e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

若

f (x) = g (x)

，则

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

使用对数计算法则:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn), x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

作图

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