What is the general solution for cos(2x+pi)=0 ?

The general solution for cos(2x+pi)=0 is x=pin-pi/2+pi/4 ,x=pin-pi/2+(3pi)/4

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cos(2x+pi)=0

Solution

cos (2 x + π) = 0

Solution

x = πn - \frac{π}{2} + \frac{π}{4}, x = πn - \frac{π}{2} + \frac{3 π}{4}

Degrees

x = - 4 5^{\circ} + 18 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x + π) = 0

General solutions for

cos (2 x + π) = 0

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x + π = \frac{π}{2} + 2 πn, 2 x + π = \frac{3 π}{2} + 2 πn

2 x + π = \frac{π}{2} + 2 πn, 2 x + π = \frac{3 π}{2} + 2 πn

Solve

2 x + π = \frac{π}{2} + 2 πn : x = πn - \frac{π}{2} + \frac{π}{4}

2 x + π = \frac{π}{2} + 2 πn

Move

π

to the right side

2 x + π = \frac{π}{2} + 2 πn

Subtract

π

from both sides

2 x + π - π = \frac{π}{2} + 2 πn - π

Simplify

2 x = \frac{π}{2} + 2 πn - π

2 x = \frac{π}{2} + 2 πn - π

Divide both sides by

2

2 x = \frac{π}{2} + 2 πn - π

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2} : πn - \frac{π}{2} + \frac{π}{4}

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Group like terms

= - \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

= - \frac{π}{2} + πn + \frac{π}{4}

Group like terms

= πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

Solve

2 x + π = \frac{3 π}{2} + 2 πn : x = πn - \frac{π}{2} + \frac{3 π}{4}

2 x + π = \frac{3 π}{2} + 2 πn

Move

π

to the right side

2 x + π = \frac{3 π}{2} + 2 πn

Subtract

π

from both sides

2 x + π - π = \frac{3 π}{2} + 2 πn - π

Simplify

2 x = \frac{3 π}{2} + 2 πn - π

2 x = \frac{3 π}{2} + 2 πn - π

Divide both sides by

2

2 x = \frac{3 π}{2} + 2 πn - π

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2} : πn - \frac{π}{2} + \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Group like terms

= - \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{3 π}{2}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 π}{4}

= - \frac{π}{2} + πn + \frac{3 π}{4}

Group like terms

= πn - \frac{π}{2} + \frac{3 π}{4}

x = πn - \frac{π}{2} + \frac{3 π}{4}

x = πn - \frac{π}{2} + \frac{3 π}{4}

x = πn - \frac{π}{2} + \frac{3 π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}, x = πn - \frac{π}{2} + \frac{3 π}{4}

Popular Examples

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csc (θ) = - \frac{5}{4}

2-sec^2(x)=0

2 - sec^{2} (x) = 0

4sin(θ)-2sqrt(2)=0

4 sin (θ) - 22 = 0

sec(θ)= 2/(sqrt(3))

sec (θ) = \frac{2}{3}

3cos(2θ)-5sin(θ)-9=-5

3 cos (2 θ) - 5 sin (θ) - 9 = - 5

Frequently Asked Questions (FAQ)

What is the general solution for cos(2x+pi)=0 ?
The general solution for cos(2x+pi)=0 is x=pin-pi/2+pi/4 ,x=pin-pi/2+(3pi)/4