What is the general solution for solvefor x,z=cos(2x+y) ?

The general solution for solvefor x,z=cos(2x+y) is x=(arccos(z))/2+pin-y/2 ,x=-(arccos(z))/2+pin-y/2

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Popular >

solvefor x,z=cos(2x+y)

Solution

solve for

x, z = cos (2 x + y)

Solution

x = \frac{arccos ( z )}{2} + πn - \frac{y}{2}, x = - \frac{arccos ( z )}{2} + πn - \frac{y}{2}

Solution steps

z = cos (2 x + y)

Switch sides

cos (2 x + y) = z

Apply trig inverse properties

cos (2 x + y) = z

General solutions for

cos (2 x + y) = z

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

2 x + y = arccos (z) + 2 πn, 2 x + y = - arccos (z) + 2 πn

2 x + y = arccos (z) + 2 πn, 2 x + y = - arccos (z) + 2 πn

Solve

2 x + y = arccos (z) + 2 πn : x = \frac{arccos ( z )}{2} + πn - \frac{y}{2}

2 x + y = arccos (z) + 2 πn

Move

y

to the right side

2 x + y = arccos (z) + 2 πn

Subtract

y

from both sides

2 x + y - y = arccos (z) + 2 πn - y

Simplify

2 x = arccos (z) + 2 πn - y

2 x = arccos (z) + 2 πn - y

Divide both sides by

2

2 x = arccos (z) + 2 πn - y

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( z )}{2} + \frac{2 πn}{2} - \frac{y}{2}

Simplify

x = \frac{arccos ( z )}{2} + πn - \frac{y}{2}

x = \frac{arccos ( z )}{2} + πn - \frac{y}{2}

Solve

2 x + y = - arccos (z) + 2 πn : x = - \frac{arccos ( z )}{2} + πn - \frac{y}{2}

2 x + y = - arccos (z) + 2 πn

Move

y

to the right side

2 x + y = - arccos (z) + 2 πn

Subtract

y

from both sides

2 x + y - y = - arccos (z) + 2 πn - y

Simplify

2 x = - arccos (z) + 2 πn - y

2 x = - arccos (z) + 2 πn - y

Divide both sides by

2

2 x = - arccos (z) + 2 πn - y

Divide both sides by

2

\frac{2 x}{2} = - \frac{arccos ( z )}{2} + \frac{2 πn}{2} - \frac{y}{2}

Simplify

x = - \frac{arccos ( z )}{2} + πn - \frac{y}{2}

x = - \frac{arccos ( z )}{2} + πn - \frac{y}{2}

x = \frac{arccos ( z )}{2} + πn - \frac{y}{2}, x = - \frac{arccos ( z )}{2} + πn - \frac{y}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,z=cos(2x+y) ?
The general solution for solvefor x,z=cos(2x+y) is x=(arccos(z))/2+pin-y/2 ,x=-(arccos(z))/2+pin-y/2