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

The general solution for csc(θ)+sqrt(2)=0 is θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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csc(θ)+sqrt(2)=0

csc (θ) + 2 = 0

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Degrees

θ = 22 5^{\circ} + 36 0^{\circ} n, θ = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) + 2 = 0

Move

2

to the right side

csc (θ) + 2 = 0

Subtract

2

from both sides

csc (θ) + 2 - 2 = 0 - 2

Simplify

csc (θ) = - 2

csc (θ) = - 2

General solutions for

csc (θ) = - 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

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

csc (x) = 2

cos (\frac{5 π}{6})

tan (- 1)

2 cos (θ) - 1 = 0

sin (x) = 0.4

What is the general solution for csc(θ)+sqrt(2)=0 ?
The general solution for csc(θ)+sqrt(2)=0 is θ=(5pi)/4+2pin,θ=(7pi)/4+2pin