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

The general solution for cos(x)= 2/(sqrt(6)) is x=0.61547…+2pin,x=2pi-0.61547…+2pin

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cos(x)= 2/(sqrt(6))

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

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn

Radians

x = 0.61547 \dots + 6.28318 \dots n, x = 5.66770 \dots + 6.28318 \dots n

Solution steps

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

Simplify

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

\frac{2}{6}

Factor

6 : 23

Factor

6 = 2 \cdot 3

= 2 \cdot 3

Apply radical rule:

n ab = n a n b

= 23

= \frac{2}{2 3}

Cancel

\frac{2}{2 3} : \frac{2}{3}

\frac{2}{2 3}

Apply radical rule:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2}{2 ^{\frac{1}{2}} 3}

Apply exponent rule:

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

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= \frac{2 ^{1 - \frac{1}{2}}}{3}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2 ^{\frac{1}{2}}}{3}

Apply radical rule:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{2}{3}

= \frac{2}{3}

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{2}{3}

Apply trig inverse properties

cos (x) = \frac{2}{3}

General solutions for

cos (x) = \frac{2}{3}

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

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

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

Show solutions in decimal form

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn

- 8 \cdot sin (0.784 + x) = 0

6 sin^{2} (x) + 5 sin (x) + 1 = 0

arcsin (x) = arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})

3 tan^{2} (x) + tan (x) = 0

tan^{2} (x) - 4 sin (x) + 4 = 0

What is the general solution for cos(x)= 2/(sqrt(6)) ?
The general solution for cos(x)= 2/(sqrt(6)) is x=0.61547…+2pin,x=2pi-0.61547…+2pin