What is the general solution for 2cos(3x)=0 ?

The general solution for 2cos(3x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3

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Popular >

2cos(3x)=0

Solution

2 cos (3 x) = 0

Solution

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Degrees

x = 3 0^{\circ} + 12 0^{\circ} n, x = 9 0^{\circ} + 12 0^{\circ} n

Solution steps

2 cos (3 x) = 0

Divide both sides by

2

2 cos (3 x) = 0

Divide both sides by

2

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

Simplify

cos (3 x) = 0

cos (3 x) = 0

General solutions for

cos (3 x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Solve

3 x = \frac{π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{3}

3 x = \frac{π}{2} + 2 πn

Divide both sides by

3

3 x = \frac{π}{2} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3} : \frac{π}{6} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

Solve

3 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{2} + \frac{2 πn}{3}

3 x = \frac{3 π}{2} + 2 πn

Divide both sides by

3

3 x = \frac{3 π}{2} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3} : \frac{π}{2} + \frac{2 πn}{3}

\frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{3 π}{2}}{3} = \frac{π}{2}

\frac{\frac{3 π}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{3 π}{6}

Cancel the common factor:

3

= \frac{π}{2}

= \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Popular Examples

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16 cos^{2} (θ) - 2 = 0

2tan^2(θ)-5tan(θ)+4=-8tan(θ)+6

2 tan^{2} (θ) - 5 tan (θ) + 4 = - 8 tan (θ) + 6

1+(tan^2(θ))/(sec(θ))=sec(θ)

1 + \frac{tan ^{2} ( θ )}{sec ( θ )} = sec (θ)

170=(160^2)/(32)sin(2θ)

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

sin(3x)=3sin(x)cos(x)

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Frequently Asked Questions (FAQ)

What is the general solution for 2cos(3x)=0 ?
The general solution for 2cos(3x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3