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受欢迎的三角函数 >

solvefor x,u=arctan(x/y)

解答

求解

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

解答

x = tan (u) y

求解步骤

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

交换两边

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

两边减去

u

arctan (\frac{x}{y}) - u = 0

用替代法求解

arctan (\frac{x}{y}) - u = 0

令

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

v - u = 0

v - u = 0 : v = u

v - u = 0

将

u

到右边

v - u = 0

两边加上

u

v - u + u = 0 + u

化简

v = u

v = u

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

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

代回

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

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

令

: v = \frac{x}{y}

arctan (v) - u = 0

将

u

到右边

arctan (v) - u = 0

两边加上

u

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

化简

arctan (v) = u

arctan (v) = u

使用反三角函数性质

arctan (v) = u

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

v = tan (u)

v = tan (u)

v = \frac{x}{y}

代回

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

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

在两边乘以

y

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

在两边乘以

y

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

化简

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

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

x = tan (u) y

作图

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