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

The general solution for tan(4x)=-1 is x=(3pi}{16}+\frac{pin)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(4x)=-1

tan (4 x) = - 1

x = \frac{3 π}{16} + \frac{πn}{4}

Degrees

x = 33.7 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{3 π}{4} + πn

4 x = \frac{3 π}{4} + πn

Solve

4 x = \frac{3 π}{4} + πn : x = \frac{3 π}{16} + \frac{πn}{4}

4 x = \frac{3 π}{4} + πn

Divide both sides by

4

4 x = \frac{3 π}{4} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{3 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{3 π}{4}}{4} + \frac{πn}{4} : \frac{3 π}{16} + \frac{πn}{4}

\frac{\frac{3 π}{4}}{4} + \frac{πn}{4}

\frac{\frac{3 π}{4}}{4} = \frac{3 π}{16}

\frac{\frac{3 π}{4}}{4}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{3 π}{16}

= \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

3 (1 - cos (3 x)) = sin^{2} (3 x)

sin (2 x) + 3 sin (x) = 0

cos (2 θ) + 10 sin^{2} (θ) = 5

9 sin^{2} (θ) - 4 = 0

sec (x) (2 cos (x) - 2) = 0

What is the general solution for tan(4x)=-1 ?
The general solution for tan(4x)=-1 is x=(3pi}{16}+\frac{pin)/4