What is the general solution for 2csc(x)+2=0 ?

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

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2csc(x)+2=0

2 csc (x) + 2 = 0

x = \frac{3 π}{2} + 2 πn

Degrees

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

Solution steps

2 csc (x) + 2 = 0

Move

2

to the right side

2 csc (x) + 2 = 0

Subtract

2

from both sides

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

Simplify

2 csc (x) = - 2

2 csc (x) = - 2

Divide both sides by

2

2 csc (x) = - 2

Divide both sides by

2

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

Simplify

csc (x) = - 1

csc (x) = - 1

General solutions for

csc (x) = - 1

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{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

1 + cos (x) = 3 cos (x)

cos (θ) = \frac{14}{16}

2 sec (x^{2}) + tan (x^{2}) - 3 = 0

5 + cos^{2} (θ) - 6 cos (θ) = 0

tan (2 c) = - tan (x)

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