What is the general solution for 3tan((θ+11pi)/6)=3 ?

The general solution for 3tan((θ+11pi)/6)=3 is θ=(3pi)/2+6pin-11pi

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3tan((θ+11pi)/6)=3

Solution

3 tan (\frac{θ + 11 π}{6}) = 3

Solution

θ = \frac{3 π}{2} + 6 πn - 11 π

Degrees

θ = - 171 0^{\circ} + 108 0^{\circ} n

Solution steps

3 tan (\frac{θ + 11 π}{6}) = 3

Divide both sides by

3

3 tan (\frac{θ + 11 π}{6}) = 3

Divide both sides by

3

\frac{3 tan ( \frac{θ + 11 π}{6} )}{3} = \frac{3}{3}

Simplify

tan (\frac{θ + 11 π}{6}) = 1

tan (\frac{θ + 11 π}{6}) = 1

General solutions for

tan (\frac{θ + 11 π}{6}) = 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{θ + 11 π}{6} = \frac{π}{4} + πn

\frac{θ + 11 π}{6} = \frac{π}{4} + πn

Solve

\frac{θ + 11 π}{6} = \frac{π}{4} + πn : θ = \frac{3 π}{2} + 6 πn - 11 π

\frac{θ + 11 π}{6} = \frac{π}{4} + πn

Multiply both sides by

6

\frac{θ + 11 π}{6} = \frac{π}{4} + πn

Multiply both sides by

6

\frac{6 ( θ + 11 π )}{6} = 6 \cdot \frac{π}{4} + 6 πn

Simplify

\frac{6 ( θ + 11 π )}{6} = 6 \cdot \frac{π}{4} + 6 πn

Simplify

\frac{6 ( θ + 11 π )}{6} : θ + 11 π

\frac{6 ( θ + 11 π )}{6}

Divide the numbers:

\frac{6}{6} = 1

= θ + 11 π

Simplify

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

6 \cdot \frac{π}{4} + 6 πn

6 \cdot \frac{π}{4} = \frac{3 π}{2}

6 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 6}{4}

Cancel the common factor:

2

= \frac{3 π}{2}

= \frac{3 π}{2} + 6 πn

θ + 11 π = \frac{3 π}{2} + 6 πn

θ + 11 π = \frac{3 π}{2} + 6 πn

θ + 11 π = \frac{3 π}{2} + 6 πn

Move

11 π

to the right side

θ + 11 π = \frac{3 π}{2} + 6 πn

Subtract

11 π

from both sides

θ + 11 π - 11 π = \frac{3 π}{2} + 6 πn - 11 π

Simplify

θ = \frac{3 π}{2} + 6 πn - 11 π

θ = \frac{3 π}{2} + 6 πn - 11 π

θ = \frac{3 π}{2} + 6 πn - 11 π

Graph

Popular Examples

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8 cos^{2} (θ) + 13 = 14 cos (θ) + 8

cos(3x)=-1/2 ,0<= x<2pi

cos (3 x) = - \frac{1}{2}, 0 \leq x < 2 π

cos(5t)=0

cos (5 t) = 0

tan(4x)=(sqrt(3))/3

tan (4 x) = \frac{3}{3}

cos(v)= 1/2

cos (v) = \frac{1}{2}

Frequently Asked Questions (FAQ)

What is the general solution for 3tan((θ+11pi)/6)=3 ?
The general solution for 3tan((θ+11pi)/6)=3 is θ=(3pi)/2+6pin-11pi