What is the general solution for 3cos(4x)=2 ?

The general solution for 3cos(4x)=2 is x=(0.84106…)/4+(pin)/2 ,x= pi/2-(0.84106…)/4+(pin)/2

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Popular >

3cos(4x)=2

Solution

3 cos (4 x) = 2

Solution

x = \frac{0.84106 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.84106 \dots}{4} + \frac{πn}{2}

Degrees

x = 12.04742 \dots^{\circ} + 9 0^{\circ} n, x = 77.95257 \dots^{\circ} + 9 0^{\circ} n

Solution steps

3 cos (4 x) = 2

Divide both sides by

3

3 cos (4 x) = 2

Divide both sides by

3

\frac{3 cos ( 4 x )}{3} = \frac{2}{3}

Simplify

cos (4 x) = \frac{2}{3}

cos (4 x) = \frac{2}{3}

Apply trig inverse properties

cos (4 x) = \frac{2}{3}

General solutions for

cos (4 x) = \frac{2}{3}

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

4 x = arccos (\frac{2}{3}) + 2 πn, 4 x = 2 π - arccos (\frac{2}{3}) + 2 πn

4 x = arccos (\frac{2}{3}) + 2 πn, 4 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

4 x = arccos (\frac{2}{3}) + 2 πn : x = \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

4 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

4

4 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

Solve

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn : x = \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

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

Divide both sides by

4

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

Divide both sides by

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4}

Cancel

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.84106 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.84106 \dots}{4} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 3cos(4x)=2 ?
The general solution for 3cos(4x)=2 is x=(0.84106…)/4+(pin)/2 ,x= pi/2-(0.84106…)/4+(pin)/2