What is the general solution for 6cos(x)+sqrt(18)=0 ?

The general solution for 6cos(x)+sqrt(18)=0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin

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Popular >

6cos(x)+sqrt(18)=0

Solution

6 cos (x) + 18 = 0

Solution

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Degrees

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

Solution steps

6 cos (x) + 18 = 0

18 = 32

18

Prime factorization of

18 : 2 \cdot 3^{2}

18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3

= 2 \cdot 3^{2}

= 3^{2} \cdot 2

Apply radical rule:

n ab = n a n b

= 2 3^{2}

Apply radical rule:

n a^{n} = a

3^{2} = 3

= 32

6 cos (x) + 32 = 0

Move

32

to the right side

6 cos (x) + 32 = 0

Subtract

32

from both sides

6 cos (x) + 32 - 32 = 0 - 32

Simplify

6 cos (x) = - 32

6 cos (x) = - 32

Divide both sides by

6

6 cos (x) = - 32

Divide both sides by

6

\frac{6 cos ( x )}{6} = \frac{- 3 2}{6}

Simplify

\frac{6 cos ( x )}{6} = \frac{- 3 2}{6}

Simplify

\frac{6 cos ( x )}{6} : cos (x)

\frac{6 cos ( x )}{6}

Divide the numbers:

\frac{6}{6} = 1

= cos (x)

Simplify

\frac{- 3 2}{6} : - \frac{2}{2}

\frac{- 3 2}{6}

Apply the fraction rule:

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

= - \frac{3 2}{6}

Cancel the common factor:

3

= - \frac{2}{2}

cos (x) = - \frac{2}{2}

cos (x) = - \frac{2}{2}

cos (x) = - \frac{2}{2}

General solutions for

cos (x) = - \frac{2}{2}

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}

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 6cos(x)+sqrt(18)=0 ?
The general solution for 6cos(x)+sqrt(18)=0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin