What is the general solution for tan((2x)/3)-1=0 ?

The general solution for tan((2x)/3)-1=0 is x=(3pi)/8+(3pin)/2

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tan((2x)/3)-1=0

Solution

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

Solution

x = \frac{3 π}{8} + \frac{3 πn}{2}

Degrees

x = 67. 5^{\circ} + 27 0^{\circ} n

Solution steps

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

Move

1

to the right side

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

Add

1

to both sides

tan (\frac{2 x}{3}) - 1 + 1 = 0 + 1

Simplify

tan (\frac{2 x}{3}) = 1

tan (\frac{2 x}{3}) = 1

General solutions for

tan (\frac{2 x}{3}) = 1

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}{4} + πn

\frac{2 x}{3} = \frac{π}{4} + πn

Solve

\frac{2 x}{3} = \frac{π}{4} + πn : x = \frac{3 π}{8} + \frac{3 πn}{2}

\frac{2 x}{3} = \frac{π}{4} + πn

Multiply both sides by

3

\frac{2 x}{3} = \frac{π}{4} + πn

Multiply both sides by

3

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

Simplify

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

3 \cdot \frac{π}{4} + 3 πn

Multiply

3 \cdot \frac{π}{4} : \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 3}{4}

= \frac{3 π}{4} + 3 πn

2 x = \frac{3 π}{4} + 3 πn

2 x = \frac{3 π}{4} + 3 πn

2 x = \frac{3 π}{4} + 3 πn

Divide both sides by

2

2 x = \frac{3 π}{4} + 3 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{3 π}{4}}{2} + \frac{3 πn}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{3 π}{4}}{2} + \frac{3 πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{3 π}{4}}{2} + \frac{3 πn}{2} : \frac{3 π}{8} + \frac{3 πn}{2}

\frac{\frac{3 π}{4}}{2} + \frac{3 πn}{2}

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{8}

\frac{\frac{3 π}{4}}{2}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{3 π}{8}

= \frac{3 π}{8} + \frac{3 πn}{2}

x = \frac{3 π}{8} + \frac{3 πn}{2}

x = \frac{3 π}{8} + \frac{3 πn}{2}

x = \frac{3 π}{8} + \frac{3 πn}{2}

x = \frac{3 π}{8} + \frac{3 πn}{2}

Graph

Popular Examples

sin(θ)-cos(θ)=1

sin (θ) - cos (θ) = 1

-5/2 csc(θ/2)=-sqrt(3)-csc(θ/2)

- \frac{5}{2} csc (\frac{θ}{2}) = - 3 - csc (\frac{θ}{2})

4cos(2θ)+11sin(θ)-4=3

4 cos (2 θ) + 11 sin (θ) - 4 = 3

sinh(x)= 7/24

sinh (x) = \frac{7}{24}

cos(x)= 5/15

cos (x) = \frac{5}{15}

Frequently Asked Questions (FAQ)

What is the general solution for tan((2x)/3)-1=0 ?
The general solution for tan((2x)/3)-1=0 is x=(3pi)/8+(3pin)/2