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Popular >

solvefor x,sin(x+xy)=0

Solution

solve for

x, sin (x + x y) = 0

Solution

x = \frac{2 πn}{1 + y}, x = \frac{π}{1 + y} + \frac{2 πn}{1 + y}; y \neq = - 1

Solution steps

sin (x + x y) = 0

General solutions for

sin (x + x y) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x + x y = 0 + 2 πn, x + x y = π + 2 πn

x + x y = 0 + 2 πn, x + x y = π + 2 πn

Solve

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

x + x y = 0 + 2 πn

0 + 2 πn = 2 πn

x + x y = 2 πn

Factor

x + x y : x (1 + y)

x + x y

Factor out common term

x

= x (1 + y)

x (1 + y) = 2 πn

Divide both sides by

1 + y; y \neq = - 1

x (1 + y) = 2 πn

Divide both sides by

1 + y; y \neq = - 1

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

Simplify

x = \frac{2 πn}{1 + y}; y \neq = - 1

x = \frac{2 πn}{1 + y}; y \neq = - 1

Solve

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

x + x y = π + 2 πn

Factor

x + x y : x (1 + y)

x + x y

Factor out common term

x

= x (1 + y)

x (1 + y) = π + 2 πn

Divide both sides by

1 + y; y \neq = - 1

x (1 + y) = π + 2 πn

Divide both sides by

1 + y; y \neq = - 1

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

Simplify

x = \frac{π}{1 + y} + \frac{2 πn}{1 + y}; y \neq = - 1

x = \frac{π}{1 + y} + \frac{2 πn}{1 + y}; y \neq = - 1

x = \frac{2 πn}{1 + y}, x = \frac{π}{1 + y} + \frac{2 πn}{1 + y}; y \neq = - 1

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