What is the general solution for tan(θ/4)+sqrt(3)=0 ?

The general solution for tan(θ/4)+sqrt(3)=0 is θ=(8pi)/3+4pin

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tan(θ/4)+sqrt(3)=0

tan (\frac{θ}{4}) + 3 = 0

θ = \frac{8 π}{3} + 4 πn

Degrees

θ = 48 0^{\circ} + 72 0^{\circ} n

Solution steps

tan (\frac{θ}{4}) + 3 = 0

Move

3

to the right side

tan (\frac{θ}{4}) + 3 = 0

Subtract

3

from both sides

tan (\frac{θ}{4}) + 3 - 3 = 0 - 3

Simplify

tan (\frac{θ}{4}) = - 3

tan (\frac{θ}{4}) = - 3

General solutions for

tan (\frac{θ}{4}) = - 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{θ}{4} = \frac{2 π}{3} + πn

\frac{θ}{4} = \frac{2 π}{3} + πn

Solve

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

\frac{θ}{4} = \frac{2 π}{3} + πn

Multiply both sides by

4

\frac{θ}{4} = \frac{2 π}{3} + πn

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

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

4 \cdot \frac{2 π}{3} + 4 πn

4 \cdot \frac{2 π}{3} = \frac{8 π}{3}

4 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 4}{3}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{8 π}{3}

= \frac{8 π}{3} + 4 πn

θ = \frac{8 π}{3} + 4 πn

θ = \frac{8 π}{3} + 4 πn

θ = \frac{8 π}{3} + 4 πn

θ = \frac{8 π}{3} + 4 πn

tan (3 r + 2) = 4 5^{\circ}

8 sin^{3} (x) - 6 sin (x) + 1 = 0

cos^{2} (z) = \frac{3}{2}

sin (x) + 2 cos (x) = - sin (3 x)

cos (x) = 0.85

What is the general solution for tan(θ/4)+sqrt(3)=0 ?
The general solution for tan(θ/4)+sqrt(3)=0 is θ=(8pi)/3+4pin