What is the general solution for 3csc(x)-2=4 ?

The general solution for 3csc(x)-2=4 is x= pi/6+2pin,x=(5pi)/6+2pin

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3csc(x)-2=4

3 csc (x) - 2 = 4

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

3 csc (x) - 2 = 4

Move

2

to the right side

3 csc (x) - 2 = 4

Add

2

to both sides

3 csc (x) - 2 + 2 = 4 + 2

Simplify

3 csc (x) = 6

3 csc (x) = 6

Divide both sides by

3

3 csc (x) = 6

Divide both sides by

3

\frac{3 csc ( x )}{3} = \frac{6}{3}

Simplify

csc (x) = 2

csc (x) = 2

General solutions for

csc (x) = 2

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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

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

csc (x) - sin (x) = cot (x) cos (x)

sec^{2} (x) + csc^{2} (x) = sec^{2} (x) csc^{2} (x)

cot^{2} (x) - cos^{2} (x) = cot^{2} (x) cos^{2} (x)

What is the general solution for 3csc(x)-2=4 ?
The general solution for 3csc(x)-2=4 is x= pi/6+2pin,x=(5pi)/6+2pin