What is the general solution for 6sqrt(2)+12cos(x-45)=0 ?

The general solution for 6sqrt(2)+12cos(x-45)=0 is x=360n+180,x=360n+270

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6sqrt(2)+12cos(x-45)=0

Solution

62 + 12 cos (x - 4 5^{\circ}) = 0

Solution

x = 36 0^{\circ} n + 18 0^{\circ}, x = 36 0^{\circ} n + 27 0^{\circ}

Radians

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

Solution steps

62 + 12 cos (x - 4 5^{\circ}) = 0

Move

62

to the right side

62 + 12 cos (x - 4 5^{\circ}) = 0

Subtract

62

from both sides

62 + 12 cos (x - 4 5^{\circ}) - 62 = 0 - 62

Simplify

12 cos (x - 4 5^{\circ}) = - 62

12 cos (x - 4 5^{\circ}) = - 62

Divide both sides by

12

12 cos (x - 4 5^{\circ}) = - 62

Divide both sides by

12

\frac{12 cos ( x - 4 5 ^{\circ} )}{12} = \frac{- 6 2}{12}

Simplify

\frac{12 cos ( x - 4 5 ^{\circ} )}{12} = \frac{- 6 2}{12}

Simplify

\frac{12 cos ( x - 4 5 ^{\circ} )}{12} : cos (x - 4 5^{\circ})

\frac{12 cos ( x - 4 5 ^{\circ} )}{12}

Divide the numbers:

\frac{12}{12} = 1

= cos (x - 4 5^{\circ})

Simplify

\frac{- 6 2}{12} : - \frac{2}{2}

\frac{- 6 2}{12}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6 2}{12}

Cancel the common factor:

6

= - \frac{2}{2}

cos (x - 4 5^{\circ}) = - \frac{2}{2}

cos (x - 4 5^{\circ}) = - \frac{2}{2}

cos (x - 4 5^{\circ}) = - \frac{2}{2}

General solutions for

cos (x - 4 5^{\circ}) = - \frac{2}{2}

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n, x - 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n

x - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n, x - 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n

Solve

x - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 18 0^{\circ}

x - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

Move

4 5^{\circ}

to the right side

x - 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

Add

4 5^{\circ}

to both sides

x - 4 5^{\circ} + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ}

Simplify

x - 4 5^{\circ} + 4 5^{\circ} = 13 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ}

Simplify

x - 4 5^{\circ} + 4 5^{\circ} : x

x - 4 5^{\circ} + 4 5^{\circ}

Add similar elements:

- 4 5^{\circ} + 4 5^{\circ} = 0

= x

Simplify

13 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ} : 36 0^{\circ} n + 18 0^{\circ}

13 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ}

Group like terms

= 36 0^{\circ} n + 4 5^{\circ} + 13 5^{\circ}

Combine the fractions

4 5^{\circ} + 13 5^{\circ} : 18 0^{\circ}

Apply rule

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

= \frac{18 0 ^{\circ} + 54 0 ^{\circ}}{4}

Add similar elements:

18 0^{\circ} + 54 0^{\circ} = 72 0^{\circ}

= 18 0^{\circ}

Divide the numbers:

\frac{4}{4} = 1

= 18 0^{\circ}

= 36 0^{\circ} n + 18 0^{\circ}

x = 36 0^{\circ} n + 18 0^{\circ}

x = 36 0^{\circ} n + 18 0^{\circ}

x = 36 0^{\circ} n + 18 0^{\circ}

Solve

x - 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 27 0^{\circ}

x - 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n

Move

4 5^{\circ}

to the right side

x - 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n

Add

4 5^{\circ}

to both sides

x - 4 5^{\circ} + 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ}

Simplify

x - 4 5^{\circ} + 4 5^{\circ} = 22 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ}

Simplify

x - 4 5^{\circ} + 4 5^{\circ} : x

x - 4 5^{\circ} + 4 5^{\circ}

Add similar elements:

- 4 5^{\circ} + 4 5^{\circ} = 0

= x

Simplify

22 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ} : 36 0^{\circ} n + 27 0^{\circ}

22 5^{\circ} + 36 0^{\circ} n + 4 5^{\circ}

Group like terms

= 36 0^{\circ} n + 4 5^{\circ} + 22 5^{\circ}

Combine the fractions

4 5^{\circ} + 22 5^{\circ} : 27 0^{\circ}

Apply rule

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

= \frac{18 0 ^{\circ} + 90 0 ^{\circ}}{4}

Add similar elements:

18 0^{\circ} + 90 0^{\circ} = 108 0^{\circ}

= 27 0^{\circ}

Cancel the common factor:

2

= 27 0^{\circ}

= 36 0^{\circ} n + 27 0^{\circ}

x = 36 0^{\circ} n + 27 0^{\circ}

x = 36 0^{\circ} n + 27 0^{\circ}

x = 36 0^{\circ} n + 27 0^{\circ}

x = 36 0^{\circ} n + 18 0^{\circ}, x = 36 0^{\circ} n + 27 0^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for 6sqrt(2)+12cos(x-45)=0 ?
The general solution for 6sqrt(2)+12cos(x-45)=0 is x=360n+180,x=360n+270