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

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

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2csc(θ)+2=0

2 csc (θ) + 2 = 0

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

2 csc (θ) + 2 = 0

Move

2

to the right side

2 csc (θ) + 2 = 0

Subtract

2

from both sides

2 csc (θ) + 2 - 2 = 0 - 2

Simplify

2 csc (θ) = - 2

2 csc (θ) = - 2

Divide both sides by

2

2 csc (θ) = - 2

Divide both sides by

2

\frac{2 csc ( θ )}{2} = \frac{- 2}{2}

Simplify

csc (θ) = - 1

csc (θ) = - 1

General solutions for

csc (θ) = - 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

θ = \frac{3 π}{2} + 2 πn

θ = \frac{3 π}{2} + 2 πn

cos (x + 2 π) = 1 - cos (x - 2 π)

sin^{4} (\frac{x}{3}) + cos^{4} (\frac{x}{3}) = \frac{5}{8}

arctan (x) = \frac{85}{( \frac{150}{2} - ( \frac{65}{4} ) )}

4 cos^{2} (2 x) = 3

- 2 sin (x) = 1

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