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

The general solution for tan(θ)= 5/(5sqrt(3)) is θ= pi/6+pin

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tan(θ)= 5/(5sqrt(3))

tan (θ) = \frac{5}{5 3}

θ = \frac{π}{6} + πn

Solution steps

tan (θ) = \frac{5}{5 3}

Simplify

\frac{5}{5 3} : \frac{3}{3}

\frac{5}{5 3}

Divide the numbers:

\frac{5}{5} = 1

= \frac{1}{3}

Rationalize

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

= \frac{3}{3}

tan (θ) = \frac{3}{3}

General solutions for

tan (θ) = \frac{3}{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}

θ = \frac{π}{6} + πn

θ = \frac{π}{6} + πn

7 cos (x) = 2 + 5 cos (x)

cos (x) = 7

5 sin (θ) cos (θ) + 4 cos (θ) = 0

2 csc (x) + 4 = 0

2 sin (x) = 3, 0 \leq x \leq 2 π

What is the general solution for tan(θ)= 5/(5sqrt(3)) ?
The general solution for tan(θ)= 5/(5sqrt(3)) is θ= pi/6+pin