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受欢迎的三角函数 >

solvefor y,x+arctan(y/x)=0

解答

求解

y, x + arctan (\frac{y}{x}) = 0

解答

y = tan (- x) x

求解步骤

x + arctan (\frac{y}{x}) = 0

用替代法求解

x + arctan (\frac{y}{x}) = 0

令

: arctan (\frac{y}{x}) = u

x + u = 0

x + u = 0 : u = - x

x + u = 0

将

x

到右边

x + u = 0

两边减去

x

x + u - x = 0 - x

化简

u = - x

u = - x

arctan (\frac{y}{x}) = - x

u = arctan (\frac{y}{x})

代回

arctan (\frac{y}{x}) = - x

arctan (\frac{y}{x}) = - x

用替代法求解

x + arctan (\frac{y}{x}) = 0

令

: arctan (\frac{y}{x}) = u

x + u = 0

x + u = 0 : u = - x

x + u = 0

将

x

到右边

x + u = 0

两边减去

x

x + u - x = 0 - x

化简

u = - x

u = - x

arctan (\frac{y}{x}) = - x

u = arctan (\frac{y}{x})

代回

arctan (\frac{y}{x}) = - x

arctan (\frac{y}{x}) = - x

令

: u = \frac{y}{x}

x + arctan (u) = 0

将

x

到右边

x + arctan (u) = 0

两边减去

x

x + arctan (u) - x = 0 - x

化简

arctan (u) = - x

arctan (u) = - x

使用反三角函数性质

arctan (u) = - x

arctan (x) = a \Rightarrow x = tan (a)

u = tan (- x)

u = tan (- x)

u = \frac{y}{x}

代回

\frac{y}{x} = tan (- x) : y = tan (- x) x; x \neq = 0

\frac{y}{x} = tan (- x)

在两边乘以

x

\frac{y}{x} = tan (- x)

在两边乘以

x

\frac{y x}{x} = tan (- x) x; x \neq = 0

化简

y = tan (- x) x; x \neq = 0

y = tan (- x) x; x \neq = 0

y = tan (- x) x

作图

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