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

The general solution for tan(θ/8)+sqrt(3)=0 is θ=(16pi)/3+8pin

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tan(θ/8)+sqrt(3)=0

tan (\frac{θ}{8}) + 3 = 0

θ = \frac{16 π}{3} + 8 πn

Degrees

θ = 96 0^{\circ} + 144 0^{\circ} n

Solution steps

tan (\frac{θ}{8}) + 3 = 0

Move

3

to the right side

tan (\frac{θ}{8}) + 3 = 0

Subtract

3

from both sides

tan (\frac{θ}{8}) + 3 - 3 = 0 - 3

Simplify

tan (\frac{θ}{8}) = - 3

tan (\frac{θ}{8}) = - 3

General solutions for

tan (\frac{θ}{8}) = - 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}{8} = \frac{2 π}{3} + πn

\frac{θ}{8} = \frac{2 π}{3} + πn

Solve

\frac{θ}{8} = \frac{2 π}{3} + πn : θ = \frac{16 π}{3} + 8 πn

\frac{θ}{8} = \frac{2 π}{3} + πn

Multiply both sides by

8

\frac{θ}{8} = \frac{2 π}{3} + πn

Multiply both sides by

8

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

Simplify

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

Simplify

\frac{8 θ}{8} : θ

\frac{8 θ}{8}

Divide the numbers:

\frac{8}{8} = 1

= θ

Simplify

8 \cdot \frac{2 π}{3} + 8 πn : \frac{16 π}{3} + 8 πn

8 \cdot \frac{2 π}{3} + 8 πn

8 \cdot \frac{2 π}{3} = \frac{16 π}{3}

8 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 8}{3}

Multiply the numbers:

2 \cdot 8 = 16

= \frac{16 π}{3}

= \frac{16 π}{3} + 8 πn

θ = \frac{16 π}{3} + 8 πn

θ = \frac{16 π}{3} + 8 πn

θ = \frac{16 π}{3} + 8 πn

θ = \frac{16 π}{3} + 8 πn

sin (\frac{θ}{2}) - 1 = 0, 0 \leq θ \leq 2 π

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

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

cos (a) = 0

cos (3 x) = \frac{- 3}{2}

What is the general solution for tan(θ/8)+sqrt(3)=0 ?
The general solution for tan(θ/8)+sqrt(3)=0 is θ=(16pi)/3+8pin