What is the general solution for 2sin(θ/3)+sqrt(3)=0 ?

The general solution for 2sin(θ/3)+sqrt(3)=0 is θ=4pi+6pin,θ=5pi+6pin

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Popular >

2sin(θ/3)+sqrt(3)=0

Solution

2 sin (\frac{θ}{3}) + 3 = 0

Solution

θ = 4 π + 6 πn, θ = 5 π + 6 πn

Degrees

θ = 72 0^{\circ} + 108 0^{\circ} n, θ = 90 0^{\circ} + 108 0^{\circ} n

Solution steps

2 sin (\frac{θ}{3}) + 3 = 0

Move

3

to the right side

2 sin (\frac{θ}{3}) + 3 = 0

Subtract

3

from both sides

2 sin (\frac{θ}{3}) + 3 - 3 = 0 - 3

Simplify

2 sin (\frac{θ}{3}) = - 3

2 sin (\frac{θ}{3}) = - 3

Divide both sides by

2

2 sin (\frac{θ}{3}) = - 3

Divide both sides by

2

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

Simplify

sin (\frac{θ}{3}) = - \frac{3}{2}

sin (\frac{θ}{3}) = - \frac{3}{2}

General solutions for

sin (\frac{θ}{3}) = - \frac{3}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{θ}{3} = \frac{4 π}{3} + 2 πn, \frac{θ}{3} = \frac{5 π}{3} + 2 πn

\frac{θ}{3} = \frac{4 π}{3} + 2 πn, \frac{θ}{3} = \frac{5 π}{3} + 2 πn

Solve

\frac{θ}{3} = \frac{4 π}{3} + 2 πn : θ = 4 π + 6 πn

\frac{θ}{3} = \frac{4 π}{3} + 2 πn

Multiply both sides by

3

\frac{θ}{3} = \frac{4 π}{3} + 2 πn

Multiply both sides by

3

\frac{3 θ}{3} = 3 \cdot \frac{4 π}{3} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} = 3 \cdot \frac{4 π}{3} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

3 \cdot \frac{4 π}{3} + 3 \cdot 2 πn : 4 π + 6 πn

3 \cdot \frac{4 π}{3} + 3 \cdot 2 πn

3 \cdot \frac{4 π}{3} = 4 π

3 \cdot \frac{4 π}{3}

Multiply fractions:

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

= \frac{4 π 3}{3}

Cancel the common factor:

3

= 4 π

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= 6 πn

= 4 π + 6 πn

θ = 4 π + 6 πn

θ = 4 π + 6 πn

θ = 4 π + 6 πn

Solve

\frac{θ}{3} = \frac{5 π}{3} + 2 πn : θ = 5 π + 6 πn

\frac{θ}{3} = \frac{5 π}{3} + 2 πn

Multiply both sides by

3

\frac{θ}{3} = \frac{5 π}{3} + 2 πn

Multiply both sides by

3

\frac{3 θ}{3} = 3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} = 3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn : 5 π + 6 πn

3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

3 \cdot \frac{5 π}{3} = 5 π

3 \cdot \frac{5 π}{3}

Multiply fractions:

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

= \frac{5 π 3}{3}

Cancel the common factor:

3

= 5 π

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= 6 πn

= 5 π + 6 πn

θ = 5 π + 6 πn

θ = 5 π + 6 πn

θ = 5 π + 6 πn

θ = 4 π + 6 πn, θ = 5 π + 6 πn

Popular Examples

6sin(4x)+4=5

6 sin (4 x) + 4 = 5

29cos(x)=-17-cos(x)

29 cos (x) = - 17 - cos (x)

2cos(x)+2cos(2x)=0

2 cos (x) + 2 cos (2 x) = 0

cos^2(x)+sin(x)=0

cos^{2} (x) + sin (x) = 0

tan(x)=(-sqrt(3))/3

tan (x) = \frac{- 3}{3}

Frequently Asked Questions (FAQ)

What is the general solution for 2sin(θ/3)+sqrt(3)=0 ?
The general solution for 2sin(θ/3)+sqrt(3)=0 is θ=4pi+6pin,θ=5pi+6pin