What is the general solution for cos(3x)= 1/3 ?

The general solution for cos(3x)= 1/3 is x=(1.23095…)/3+(2pin)/3 ,x=(2pi)/3-(1.23095…)/3+(2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(3x)= 1/3

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

x = \frac{1.23095 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.23095 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 23.50959 \dots^{\circ} + 12 0^{\circ} n, x = 96.49040 \dots^{\circ} + 12 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Solve

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

3 x = arccos (\frac{1}{3}) + 2 πn

Divide both sides by

3

3 x = arccos (\frac{1}{3}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

Solve

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

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

Divide both sides by

3

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

Divide both sides by

3

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{1.23095 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.23095 \dots}{3} + \frac{2 πn}{3}

sin (θ) = \frac{7}{8}

sin (x) = \frac{- 2}{3}

4 + 4 cos (x) = - 6 cos (x)

2 cos (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

sin (A) = \frac{4}{5}

What is the general solution for cos(3x)= 1/3 ?
The general solution for cos(3x)= 1/3 is x=(1.23095…)/3+(2pin)/3 ,x=(2pi)/3-(1.23095…)/3+(2pin)/3