What is the general solution for tan((2x)/3)-sqrt(3)=0 ?

The general solution for tan((2x)/3)-sqrt(3)=0 is x= pi/2+(3pin)/2

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tan((2x)/3)-sqrt(3)=0

Solution

tan (\frac{2 x}{3}) - 3 = 0

Solution

x = \frac{π}{2} + \frac{3 πn}{2}

Degrees

x = 9 0^{\circ} + 27 0^{\circ} n

Solution steps

tan (\frac{2 x}{3}) - 3 = 0

Move

3

to the right side

tan (\frac{2 x}{3}) - 3 = 0

Add

3

to both sides

tan (\frac{2 x}{3}) - 3 + 3 = 0 + 3

Simplify

tan (\frac{2 x}{3}) = 3

tan (\frac{2 x}{3}) = 3

General solutions for

tan (\frac{2 x}{3}) = 3

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

\frac{2 x}{3} = \frac{π}{3} + πn

\frac{2 x}{3} = \frac{π}{3} + πn

Solve

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

\frac{2 x}{3} = \frac{π}{3} + πn

Multiply both sides by

3

\frac{2 x}{3} = \frac{π}{3} + πn

Multiply both sides by

3

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

Simplify

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

Simplify

\frac{3 \cdot 2 x}{3} : 2 x

\frac{3 \cdot 2 x}{3}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 x}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2 x

Simplify

3 \cdot \frac{π}{3} + 3 πn : π + 3 πn

3 \cdot \frac{π}{3} + 3 πn

3 \cdot \frac{π}{3} = π

3 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 3}{3}

Cancel the common factor:

3

= π

= π + 3 πn

2 x = π + 3 πn

2 x = π + 3 πn

2 x = π + 3 πn

Divide both sides by

2

2 x = π + 3 πn

Divide both sides by

2

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

Simplify

x = \frac{π}{2} + \frac{3 πn}{2}

x = \frac{π}{2} + \frac{3 πn}{2}

x = \frac{π}{2} + \frac{3 πn}{2}

Popular Examples

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

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

cos(3x)*3=0

cos (3 x) \cdot 3 = 0

16sec^2(θ)-25=0

16 sec^{2} (θ) - 25 = 0

2csc^2(x)-4=0

2 csc^{2} (x) - 4 = 0

2sin^2(θ)-3sin(θ)-2=0,0<= θ<= 2pi

2 sin^{2} (θ) - 3 sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for tan((2x)/3)-sqrt(3)=0 ?
The general solution for tan((2x)/3)-sqrt(3)=0 is x= pi/2+(3pin)/2