What is the general solution for 6cos(x)=-3sqrt(2) ?

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

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6cos(x)=-3sqrt(2)

6 cos (x) = - 32

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) = - 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

cos (x) = \frac{7}{12}

5 tan (x) + 3 = 4 (1 + tan (x))

cos (x) + 2 = 3

9 sin (b) + 3 = 5 sin (b) + 1

4 tan (x) + 2 sin (x) cos (x) = 0

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