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人気のある三角関数 >

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

解

解く

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

解

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}

解答ステップ

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

辺を交換する

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

以下で両辺を割る

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

以下で両辺を割る

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}

簡素化

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}

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

解く

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

以下で両辺を割る

5

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

以下で両辺を割る

5

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

簡素化

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}

解く

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

以下で両辺を割る

5

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

以下で両辺を割る

5

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

簡素化

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}

グラフ

人気の例

cot (x) = - 0.465

sin(θ)=2sqrt(2)

sin (θ) = 22

9.2sin(t)+23.2=14.365

9.2 sin (t) + 23.2 = 14.365

-2sin(x)+cos(2x)=0

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solvefor X,4cos(X)cos(Y)=3

so l v e f or X, 4 cos (X) cos (Y) = 3