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

The general solution for 6cos(x)+2=0 is x=1.91063…+2pin,x=-1.91063…+2pin

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6cos(x)+2=0

6 cos (x) + 2 = 0

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Degrees

x = 109.47122 \dots^{\circ} + 36 0^{\circ} n, x = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

6 cos (x) + 2 = 0

Move

2

to the right side

6 cos (x) + 2 = 0

Subtract

2

from both sides

6 cos (x) + 2 - 2 = 0 - 2

Simplify

6 cos (x) = - 2

6 cos (x) = - 2

Divide both sides by

6

6 cos (x) = - 2

Divide both sides by

6

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

Simplify

\frac{6 cos ( x )}{6} = \frac{- 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{- 2}{6} : - \frac{1}{3}

\frac{- 2}{6}

Apply the fraction rule:

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

= - \frac{2}{6}

Cancel the common factor:

2

= - \frac{1}{3}

cos (x) = - \frac{1}{3}

cos (x) = - \frac{1}{3}

cos (x) = - \frac{1}{3}

Apply trig inverse properties

cos (x) = - \frac{1}{3}

General solutions for

cos (x) = - \frac{1}{3}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

3 cos^{2} (θ) - 3 = sin^{2} (θ)

y, ln (sin^{2} (3 x)) = e^{x} + arccot (y)

tan (x) = a

3 tan^{2} (x) = 2 sec^{2} (x) + 1

cos (A) = \frac{8}{15}

What is the general solution for 6cos(x)+2=0 ?
The general solution for 6cos(x)+2=0 is x=1.91063…+2pin,x=-1.91063…+2pin