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受欢迎的三角函数 >

solvefor x,(sin(pix)+cos(piy))^5=36

解答

求解

x, (sin (π x) + cos (π y))^{5} = 36

解答

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n, x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

求解步骤

(sin (π x) + cos (π y))^{5} = 36

对于

(g (x))^{n} = f (a)

，n 为奇数，解为

g (x) = n f (a)

解

sin (π x) + cos (π y) = 536 : sin (π x) = 536 - cos (π y)

sin (π x) + cos (π y) = 536

将

cos (π y)

到右边

sin (π x) + cos (π y) = 536

两边减去

cos (π y)

sin (π x) + cos (π y) - cos (π y) = 536 - cos (π y)

化简

sin (π x) = 536 - cos (π y)

sin (π x) = 536 - cos (π y)

解是

sin (π x) = 536 - cos (π y)

使用反三角函数性质

sin (π x) = 536 - cos (π y)

sin (π x) = 536 - cos (π y)

的通解

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

π x = arcsin (536 - cos (π y)) + 2 πn, π x = π + arcsin (- 536 + cos (π y)) + 2 πn

π x = arcsin (536 - cos (π y)) + 2 πn, π x = π + arcsin (- 536 + cos (π y)) + 2 πn

解

π x = arcsin (536 - cos (π y)) + 2 πn : x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n

π x = arcsin (536 - cos (π y)) + 2 πn

两边除以

π

π x = arcsin (536 - cos (π y)) + 2 πn

两边除以

π

\frac{π x}{π} = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + \frac{2 πn}{π}

化简

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n

解

π x = π + arcsin (- 536 + cos (π y)) + 2 πn : x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

π x = π + arcsin (- 536 + cos (π y)) + 2 πn

两边除以

π

π x = π + arcsin (- 536 + cos (π y)) + 2 πn

两边除以

π

\frac{π x}{π} = \frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} = \frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π} : 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

\frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π}

使用法则

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{arcsin ( cos ( π y ) - 5 36 )}{π} + \frac{2 πn}{π}

消掉

\frac{2 πn}{π} : 2 n

\frac{2 πn}{π}

约分:

π

= 2 n

= 1 + \frac{arcsin ( cos ( π y ) - 5 36 )}{π} + 2 n

x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n, x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

作图

流行的例子

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(cos(x))/(sin(x))=-0.05467

\frac{cos ( x )}{sin ( x )} = - 0.05467

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