What is the general solution for tan(4x)=1 ?

The general solution for tan(4x)=1 is x= pi/(16)+(pin)/4

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tan(4x)=1

tan (4 x) = 1

x = \frac{π}{16} + \frac{πn}{4}

Degrees

x = 11.2 5^{\circ} + 4 5^{\circ} n

Solution steps

tan (4 x) = 1

General solutions for

tan (4 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}

4 x = \frac{π}{4} + πn

4 x = \frac{π}{4} + πn

Solve

4 x = \frac{π}{4} + πn : x = \frac{π}{16} + \frac{πn}{4}

4 x = \frac{π}{4} + πn

Divide both sides by

4

4 x = \frac{π}{4} + πn

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{π}{4}}{4} + \frac{πn}{4} : \frac{π}{16} + \frac{πn}{4}

\frac{\frac{π}{4}}{4} + \frac{πn}{4}

\frac{\frac{π}{4}}{4} = \frac{π}{16}

\frac{\frac{π}{4}}{4}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{π}{16}

= \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

cos (3 x) + cos (x) = 0

cos^{2} (x) = sin (x)

2 cos^{2} (x) = 1 + sin (x)

(cot (θ) - 1) (sin (θ) + 1) = 0

sin (θ) = - \frac{3}{5}

What is the general solution for tan(4x)=1 ?
The general solution for tan(4x)=1 is x= pi/(16)+(pin)/4