What is the general solution for tan(5x)=1 ?

The general solution for tan(5x)=1 is x= pi/(20)+(pin)/5

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tan(5x)=1

tan (5 x) = 1

x = \frac{π}{20} + \frac{πn}{5}

Degrees

x = 9^{\circ} + 3 6^{\circ} n

Solution steps

tan (5 x) = 1

General solutions for

tan (5 x) = 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}

5 x = \frac{π}{4} + πn

5 x = \frac{π}{4} + πn

Solve

5 x = \frac{π}{4} + πn : x = \frac{π}{20} + \frac{πn}{5}

5 x = \frac{π}{4} + πn

Divide both sides by

5

5 x = \frac{π}{4} + πn

Divide both sides by

5

\frac{5 x}{5} = \frac{\frac{π}{4}}{5} + \frac{πn}{5}

Simplify

\frac{5 x}{5} = \frac{\frac{π}{4}}{5} + \frac{πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{π}{4}}{5} + \frac{πn}{5} : \frac{π}{20} + \frac{πn}{5}

\frac{\frac{π}{4}}{5} + \frac{πn}{5}

\frac{\frac{π}{4}}{5} = \frac{π}{20}

\frac{\frac{π}{4}}{5}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 5}

Multiply the numbers:

4 \cdot 5 = 20

= \frac{π}{20}

= \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

sec (5 x) = 2

5 sin (θ) - 1 = 3 sin (θ)

2 cos^{2} (w) - cos (w) - 1 = 0

3 csc (θ) - 3 = 0

2 sin (x) + (sin (x))^{2} = 0

What is the general solution for tan(5x)=1 ?
The general solution for tan(5x)=1 is x= pi/(20)+(pin)/5