What is the general solution for -3-6cos(x)=0 ?

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

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-3-6cos(x)=0

- 3 - 6 cos (x) = 0

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

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

- 3 - 6 cos (x) = 0

Move

3

to the right side

- 3 - 6 cos (x) = 0

Add

3

to both sides

- 3 - 6 cos (x) + 3 = 0 + 3

Simplify

- 6 cos (x) = 3

- 6 cos (x) = 3

Divide both sides by

- 6

- 6 cos (x) = 3

Divide both sides by

- 6

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

Simplify

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

Simplify

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

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

Apply the fraction rule:

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

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

Divide the numbers:

\frac{6}{6} = 1

= cos (x)

Simplify

\frac{3}{- 6} : - \frac{1}{2}

\frac{3}{- 6}

Apply the fraction rule:

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

= - \frac{3}{6}

Cancel the common factor:

3

= - \frac{1}{2}

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

General solutions for

cos (x) = - \frac{1}{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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

tan (θ) = \frac{26}{53}

n, y = - sin (2 (\frac{π}{4} + πn)) 2

tan (a) = \frac{7}{24}

2 cos^{2} (t) tan (t) - tan (t) = 0

3 = 2 - 2 sin (x)

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