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受欢迎的三角函数 >

solvefor x,r-2s+t=sin(2x+3y)

解答

求解

x, r - 2 s + t = sin (2 x + 3 y)

解答

x = \frac{arcsin ( r - 2 s + t )}{2} + πn - \frac{3 y}{2}, x = \frac{π}{2} + \frac{arcsin ( - r + 2 s - t )}{2} + πn - \frac{3 y}{2}

求解步骤

r - 2 s + t = sin (2 x + 3 y)

交换两边

sin (2 x + 3 y) = r - 2 s + t

使用反三角函数性质

sin (2 x + 3 y) = r - 2 s + t

sin (2 x + 3 y) = r - 2 s + t

的通解

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

2 x + 3 y = arcsin (r - 2 s + t) + 2 πn, 2 x + 3 y = π + arcsin (- r + 2 s - t) + 2 πn

2 x + 3 y = arcsin (r - 2 s + t) + 2 πn, 2 x + 3 y = π + arcsin (- r + 2 s - t) + 2 πn

解

2 x + 3 y = arcsin (r - 2 s + t) + 2 πn : x = \frac{arcsin ( r - 2 s + t )}{2} + πn - \frac{3 y}{2}

2 x + 3 y = arcsin (r - 2 s + t) + 2 πn

将

3 y

到右边

2 x + 3 y = arcsin (r - 2 s + t) + 2 πn

两边减去

3 y

2 x + 3 y - 3 y = arcsin (r - 2 s + t) + 2 πn - 3 y

化简

2 x = arcsin (r - 2 s + t) + 2 πn - 3 y

2 x = arcsin (r - 2 s + t) + 2 πn - 3 y

两边除以

2

2 x = arcsin (r - 2 s + t) + 2 πn - 3 y

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( r - 2 s + t )}{2} + \frac{2 πn}{2} - \frac{3 y}{2}

化简

x = \frac{arcsin ( r - 2 s + t )}{2} + πn - \frac{3 y}{2}

x = \frac{arcsin ( r - 2 s + t )}{2} + πn - \frac{3 y}{2}

解

2 x + 3 y = π + arcsin (- r + 2 s - t) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( - r + 2 s - t )}{2} + πn - \frac{3 y}{2}

2 x + 3 y = π + arcsin (- r + 2 s - t) + 2 πn

将

3 y

到右边

2 x + 3 y = π + arcsin (- r + 2 s - t) + 2 πn

两边减去

3 y

2 x + 3 y - 3 y = π + arcsin (- r + 2 s - t) + 2 πn - 3 y

化简

2 x = π + arcsin (- r + 2 s - t) + 2 πn - 3 y

2 x = π + arcsin (- r + 2 s - t) + 2 πn - 3 y

两边除以

2

2 x = π + arcsin (- r + 2 s - t) + 2 πn - 3 y

两边除以

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - r + 2 s - t )}{2} + \frac{2 πn}{2} - \frac{3 y}{2}

化简

x = \frac{π}{2} + \frac{arcsin ( - r + 2 s - t )}{2} + πn - \frac{3 y}{2}

x = \frac{π}{2} + \frac{arcsin ( - r + 2 s - t )}{2} + πn - \frac{3 y}{2}

x = \frac{arcsin ( r - 2 s + t )}{2} + πn - \frac{3 y}{2}, x = \frac{π}{2} + \frac{arcsin ( - r + 2 s - t )}{2} + πn - \frac{3 y}{2}

作图

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