What is the general solution for sqrt(3)csc(x)-2=0 ?

The general solution for sqrt(3)csc(x)-2=0 is x= pi/3+2pin,x=(2pi)/3+2pin

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sqrt(3)csc(x)-2=0

3 csc (x) - 2 = 0

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

3 csc (x) - 2 = 0

Move

2

to the right side

3 csc (x) - 2 = 0

Add

2

to both sides

3 csc (x) - 2 + 2 = 0 + 2

Simplify

3 csc (x) = 2

3 csc (x) = 2

Divide both sides by

3

3 csc (x) = 2

Divide both sides by

3

\frac{3 csc ( x )}{3} = \frac{2}{3}

Simplify

\frac{3 csc ( x )}{3} = \frac{2}{3}

Simplify

\frac{3 csc ( x )}{3} : csc (x)

\frac{3 csc ( x )}{3}

Cancel the common factor:

3

= csc (x)

Simplify

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

csc (x) = \frac{2 3}{3}

csc (x) = \frac{2 3}{3}

csc (x) = \frac{2 3}{3}

General solutions for

csc (x) = \frac{2 3}{3}

csc (x)

periodicity table with

2 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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

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

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

cot (x) = 1

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

cot (x) = - 1

cos (x) = 0, 0 \leq x \leq 2 π

cos (x) = 2

What is the general solution for sqrt(3)csc(x)-2=0 ?
The general solution for sqrt(3)csc(x)-2=0 is x= pi/3+2pin,x=(2pi)/3+2pin