What is the general solution for cot(x/2)=-1 ?

The general solution for cot(x/2)=-1 is x=(3pi)/2+2pin

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cot(x/2)=-1

cot (\frac{x}{2}) = - 1

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

cot (\frac{x}{2}) = - 1

General solutions for

cot (\frac{x}{2}) = - 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

\frac{x}{2} = \frac{3 π}{4} + πn

\frac{x}{2} = \frac{3 π}{4} + πn

Solve

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

\frac{x}{2} = \frac{3 π}{4} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{3 π}{4} + πn

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

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

2 \cdot \frac{3 π}{4} + 2 πn

2 \cdot \frac{3 π}{4} = \frac{3 π}{2}

2 \cdot \frac{3 π}{4}

Multiply fractions:

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

= \frac{3 π 2}{4}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 π}{4}

Cancel the common factor:

2

= \frac{3 π}{2}

= \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

5 sin (\frac{2 x - π}{2}) = 0.5

16 sin^{2} (θ) = 12

tan (θ) = - \frac{57}{9}

sin^{2} (x) = \frac{2}{3}

sin (4 y) + sin (6 y) + cos (y) = 0

What is the general solution for cot(x/2)=-1 ?
The general solution for cot(x/2)=-1 is x=(3pi)/2+2pin