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

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

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Popular >

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

Solution

6 cos (A) + 18 = 0

Solution

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

Degrees

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

Solution steps

6 cos (A) + 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:

= 2 3^{2}

Apply radical rule:

3^{2} = 3

= 32

6 cos (A) + 32 = 0

Move

32

to the right side

6 cos (A) + 32 = 0

Subtract

32

from both sides

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

Simplify

6 cos (A) = - 32

6 cos (A) = - 32

Divide both sides by

6

6 cos (A) = - 32

Divide both sides by

6

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

Simplify

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

Simplify

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

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

Divide the numbers:

\frac{6}{6} = 1

= cos (A)

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 (A) = - \frac{2}{2}

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

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

General solutions for

cos (A) = - \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}

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

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

Popular Examples

csc(θ)=(sqrt(5))/2

csc (θ) = \frac{5}{2}

sin(θ)+3=5sin(θ)

sin (θ) + 3 = 5 sin (θ)

2sin^2(x)-cos(2x)=0

2 sin^{2} (x) - cos (2 x) = 0

csc(x)cos^2(x)+sin^2(x)=csc(x)

csc (x) cos^{2} (x) + sin^{2} (x) = csc (x)

0.87=5cos(3x)

0.87 = 5 cos (3 x)

Frequently Asked Questions (FAQ)

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