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

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

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4tan(4θ)=4

4 tan (4 θ) = 4

θ = \frac{π}{16} + \frac{πn}{4}

Degrees

θ = 11.2 5^{\circ} + 4 5^{\circ} n

Solution steps

4 tan (4 θ) = 4

Divide both sides by

4

4 tan (4 θ) = 4

Divide both sides by

4

\frac{4 tan ( 4 θ )}{4} = \frac{4}{4}

Simplify

tan (4 θ) = 1

tan (4 θ) = 1

General solutions for

tan (4 θ) = 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 θ = \frac{π}{4} + πn

4 θ = \frac{π}{4} + πn

Solve

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

4 θ = \frac{π}{4} + πn

Divide both sides by

4

4 θ = \frac{π}{4} + πn

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

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}

θ = \frac{π}{16} + \frac{πn}{4}

θ = \frac{π}{16} + \frac{πn}{4}

θ = \frac{π}{16} + \frac{πn}{4}

θ = \frac{π}{16} + \frac{πn}{4}

sin (2 x) = \frac{( 10 m - 5 )}{2}

3 sin^{2} (θ) - 2 sin (θ) = 2

2 - sin (x) tan (x) = cos (x)

tan (2 x - \frac{n}{4}) = - 1, 0^{\circ} < x \leq 36 0^{\circ}

2 sin^{2} (θ) = cos^{2} (θ)

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