What is the general solution for tan(θ/5)+sqrt(3)=0 ?

The general solution for tan(θ/5)+sqrt(3)=0 is θ=(10pi)/3+5pin

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tan(θ/5)+sqrt(3)=0

tan (\frac{θ}{5}) + 3 = 0

θ = \frac{10 π}{3} + 5 πn

Degrees

θ = 60 0^{\circ} + 90 0^{\circ} n

Solution steps

tan (\frac{θ}{5}) + 3 = 0

Move

3

to the right side

tan (\frac{θ}{5}) + 3 = 0

Subtract

3

from both sides

tan (\frac{θ}{5}) + 3 - 3 = 0 - 3

Simplify

tan (\frac{θ}{5}) = - 3

tan (\frac{θ}{5}) = - 3

General solutions for

tan (\frac{θ}{5}) = - 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}{5} = \frac{2 π}{3} + πn

\frac{θ}{5} = \frac{2 π}{3} + πn

Solve

\frac{θ}{5} = \frac{2 π}{3} + πn : θ = \frac{10 π}{3} + 5 πn

\frac{θ}{5} = \frac{2 π}{3} + πn

Multiply both sides by

5

\frac{θ}{5} = \frac{2 π}{3} + πn

Multiply both sides by

5

\frac{5 θ}{5} = 5 \cdot \frac{2 π}{3} + 5 πn

Simplify

\frac{5 θ}{5} = 5 \cdot \frac{2 π}{3} + 5 πn

Simplify

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Divide the numbers:

\frac{5}{5} = 1

= θ

Simplify

5 \cdot \frac{2 π}{3} + 5 πn : \frac{10 π}{3} + 5 πn

5 \cdot \frac{2 π}{3} + 5 πn

5 \cdot \frac{2 π}{3} = \frac{10 π}{3}

5 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 5}{3}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{10 π}{3}

= \frac{10 π}{3} + 5 πn

θ = \frac{10 π}{3} + 5 πn

θ = \frac{10 π}{3} + 5 πn

θ = \frac{10 π}{3} + 5 πn

θ = \frac{10 π}{3} + 5 πn

3 tan (x) - 3 = 0, 0 \leq x < 2 π

sec^{2} (θ) = 2

sin^{2} (θ) = 8 - 2 cos^{2} (θ)

10 sin (x) + 16 = 3 sin (x) + 9

2 sin (5 θ) = 0

What is the general solution for tan(θ/5)+sqrt(3)=0 ?
The general solution for tan(θ/5)+sqrt(3)=0 is θ=(10pi)/3+5pin