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

The general solution for 2-6cos(x)=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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2-6cos(x)=0

2 - 6 cos (x) = 0

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Degrees

x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 - 6 cos (x) = 0

Move

2

to the right side

2 - 6 cos (x) = 0

Subtract

2

from both sides

2 - 6 cos (x) - 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}

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{- 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 = 2 π - arccos (a) + 2 πn

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

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

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

sec^{2} (x) tan^{2} (x) = sin^{2} (x)

12 sin^{2} (θ) = 3

4 sin^{2} (θ) + 2 cos^{2} (θ) = 3

ω = 360 l b \cdot 5 sec (x)

u, x = 2 cos (u) cos (v)

What is the general solution for 2-6cos(x)=0 ?
The general solution for 2-6cos(x)=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin