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受欢迎的三角函数 >

solvefor y,sin(xy)=x

解答

求解

y, sin (x y) = x

解答

y = \frac{arcsin ( x )}{x} + \frac{2 πn}{x}, y = \frac{π}{x} + \frac{arcsin ( - x )}{x} + \frac{2 πn}{x}

求解步骤

sin (x y) = x

使用反三角函数性质

sin (x y) = x

sin (x y) = x

的通解

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

x y = arcsin (x) + 2 πn, x y = π + arcsin (- x) + 2 πn

x y = arcsin (x) + 2 πn, x y = π + arcsin (- x) + 2 πn

解

x y = arcsin (x) + 2 πn : y = \frac{arcsin ( x )}{x} + \frac{2 πn}{x}; x \neq = 0

x y = arcsin (x) + 2 πn

两边除以

x; x \neq = 0

x y = arcsin (x) + 2 πn

两边除以

x; x \neq = 0

\frac{x y}{x} = \frac{arcsin ( x )}{x} + \frac{2 πn}{x}; x \neq = 0

化简

y = \frac{arcsin ( x )}{x} + \frac{2 πn}{x}; x \neq = 0

y = \frac{arcsin ( x )}{x} + \frac{2 πn}{x}; x \neq = 0

解

x y = π + arcsin (- x) + 2 πn : y = \frac{π}{x} + \frac{arcsin ( - x )}{x} + \frac{2 πn}{x}; x \neq = 0

x y = π + arcsin (- x) + 2 πn

两边除以

x; x \neq = 0

x y = π + arcsin (- x) + 2 πn

两边除以

x; x \neq = 0

\frac{x y}{x} = \frac{π}{x} + \frac{arcsin ( - x )}{x} + \frac{2 πn}{x}; x \neq = 0

化简

y = \frac{π}{x} + \frac{arcsin ( - x )}{x} + \frac{2 πn}{x}; x \neq = 0

y = \frac{π}{x} + \frac{arcsin ( - x )}{x} + \frac{2 πn}{x}; x \neq = 0

y = \frac{arcsin ( x )}{x} + \frac{2 πn}{x}, y = \frac{π}{x} + \frac{arcsin ( - x )}{x} + \frac{2 πn}{x}

作图

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