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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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:

= 23

= \frac{2}{2 3}

Cancel

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

\frac{2}{2 3}

Apply radical rule:

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:

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

16 sin^{2} (x) = 9

tan (x) - cos (x) = 0

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

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

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