What is the general solution for cot(2x)=-1,(0,2pi) ?

The general solution for cot(2x)=-1,(0,2pi) is x=(3pi)/8 ,x=(7pi)/8 ,x=(11pi)/8 ,x=(15pi)/8

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cot(2x)=-1,(0,2pi)

cot (2 x) = - 1, (0, 2 π)

x = \frac{3 π}{8}, x = \frac{7 π}{8}, x = \frac{11 π}{8}, x = \frac{15 π}{8}

Degrees

x = 67. 5^{\circ}, x = 157. 5^{\circ}, x = 247. 5^{\circ}, x = 337. 5^{\circ}

Solution steps

cot (2 x) = - 1, (0, 2 π)

General solutions for

cot (2 x) = - 1

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

2 x = \frac{3 π}{4} + πn

2 x = \frac{3 π}{4} + πn

Solve

2 x = \frac{3 π}{4} + πn : x = \frac{3 π}{8} + \frac{πn}{2}

2 x = \frac{3 π}{4} + πn

Divide both sides by

2

2 x = \frac{3 π}{4} + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{3 π}{4}}{2} + \frac{πn}{2} : \frac{3 π}{8} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{8}

\frac{\frac{3 π}{4}}{2}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{3 π}{8}

= \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

Solutions for the range

(0, 2 π)

x = \frac{3 π}{8}, x = \frac{7 π}{8}, x = \frac{11 π}{8}, x = \frac{15 π}{8}

What is the general solution for cot(2x)=-1,(0,2pi) ?
The general solution for cot(2x)=-1,(0,2pi) is x=(3pi)/8 ,x=(7pi)/8 ,x=(11pi)/8 ,x=(15pi)/8