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受欢迎的三角函数 >

solvefor x,z=sin(5x)cos(5y)

解答

求解

x, z = sin (5 x) cos (5 y)

解答

x = \frac{arcsin ( \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}, x = \frac{π}{5} + \frac{arcsin ( - \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

求解步骤

z = sin (5 x) cos (5 y)

交换两边

sin (5 x) cos (5 y) = z

两边除以

cos (5 y); y \neq = \frac{π}{10} + \frac{2 πn}{5}, y \neq = \frac{3 π}{10} + \frac{2 πn}{5}

sin (5 x) cos (5 y) = z

两边除以

cos (5 y); y \neq = \frac{π}{10} + \frac{2 πn}{5}, y \neq = \frac{3 π}{10} + \frac{2 πn}{5}

\frac{sin ( 5 x ) cos ( 5 y )}{cos ( 5 y )} = \frac{z}{cos ( 5 y )}; y \neq = \frac{π}{10} + \frac{2 πn}{5}, y \neq = \frac{3 π}{10} + \frac{2 πn}{5}

化简

sin (5 x) = \frac{z}{cos ( 5 y )}; y \neq = \frac{π}{10} + \frac{2 πn}{5}, y \neq = \frac{3 π}{10} + \frac{2 πn}{5}

sin (5 x) = \frac{z}{cos ( 5 y )}; y \neq = \frac{π}{10} + \frac{2 πn}{5}, y \neq = \frac{3 π}{10} + \frac{2 πn}{5}

使用反三角函数性质

sin (5 x) = \frac{z}{cos ( 5 y )}

sin (5 x) = \frac{z}{cos ( 5 y )}

的通解

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

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

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

解

5 x = arcsin (\frac{z}{cos ( 5 y )}) + 2 πn : x = \frac{arcsin ( \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

5 x = arcsin (\frac{z}{cos ( 5 y )}) + 2 πn

两边除以

5

5 x = arcsin (\frac{z}{cos ( 5 y )}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{arcsin ( \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

化简

x = \frac{arcsin ( \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

x = \frac{arcsin ( \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

解

5 x = π + arcsin (- \frac{z}{cos ( 5 y )}) + 2 πn : x = \frac{π}{5} + \frac{arcsin ( - \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

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

两边除以

5

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

两边除以

5

\frac{5 x}{5} = \frac{π}{5} + \frac{arcsin ( - \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

化简

x = \frac{π}{5} + \frac{arcsin ( - \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

x = \frac{π}{5} + \frac{arcsin ( - \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

x = \frac{arcsin ( \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}, x = \frac{π}{5} + \frac{arcsin ( - \frac{z}{c o s ( 5 y )} )}{5} + \frac{2 πn}{5}

作图

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