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Popular >

solvefor x,y+sin(xy)=1

Solution

solve for

x, y + sin (x y) = 1

Solution

x = \frac{arcsin ( 1 - y )}{y} + \frac{2 πn}{y}, x = \frac{π}{y} + \frac{arcsin ( - 1 + y )}{y} + \frac{2 πn}{y}

Solution steps

y + sin (x y) = 1

Move

y

to the right side

y + sin (x y) = 1

Subtract

y

from both sides

y + sin (x y) - y = 1 - y

Simplify

sin (x y) = 1 - y

sin (x y) = 1 - y

Apply trig inverse properties

sin (x y) = 1 - y

General solutions for

sin (x y) = 1 - y

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

x y = arcsin (1 - y) + 2 πn, x y = π + arcsin (- 1 + y) + 2 πn

x y = arcsin (1 - y) + 2 πn, x y = π + arcsin (- 1 + y) + 2 πn

Solve

x y = arcsin (1 - y) + 2 πn : x = \frac{arcsin ( 1 - y )}{y} + \frac{2 πn}{y}; y \neq = 0

x y = arcsin (1 - y) + 2 πn

Divide both sides by

y; y \neq = 0

x y = arcsin (1 - y) + 2 πn

Divide both sides by

y; y \neq = 0

\frac{x y}{y} = \frac{arcsin ( 1 - y )}{y} + \frac{2 πn}{y}; y \neq = 0

Simplify

x = \frac{arcsin ( 1 - y )}{y} + \frac{2 πn}{y}; y \neq = 0

x = \frac{arcsin ( 1 - y )}{y} + \frac{2 πn}{y}; y \neq = 0

Solve

x y = π + arcsin (- 1 + y) + 2 πn : x = \frac{π}{y} + \frac{arcsin ( - 1 + y )}{y} + \frac{2 πn}{y}; y \neq = 0

x y = π + arcsin (- 1 + y) + 2 πn

Divide both sides by

y; y \neq = 0

x y = π + arcsin (- 1 + y) + 2 πn

Divide both sides by

y; y \neq = 0

\frac{x y}{y} = \frac{π}{y} + \frac{arcsin ( - 1 + y )}{y} + \frac{2 πn}{y}; y \neq = 0

Simplify

x = \frac{π}{y} + \frac{arcsin ( - 1 + y )}{y} + \frac{2 πn}{y}; y \neq = 0

x = \frac{π}{y} + \frac{arcsin ( - 1 + y )}{y} + \frac{2 πn}{y}; y \neq = 0

x = \frac{arcsin ( 1 - y )}{y} + \frac{2 πn}{y}, x = \frac{π}{y} + \frac{arcsin ( - 1 + y )}{y} + \frac{2 πn}{y}

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