What is the general solution for csc(θ)+1=0,(0,2pi) ?

The general solution for csc(θ)+1=0,(0,2pi) is θ=(3pi)/2

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csc(θ)+1=0,(0,2pi)

csc (θ) + 1 = 0, (0, 2 π)

θ = \frac{3 π}{2}

Degrees

θ = 27 0^{\circ}

Solution steps

csc (θ) + 1 = 0, (0, 2 π)

Move

1

to the right side

csc (θ) + 1 = 0

Subtract

1

from both sides

csc (θ) + 1 - 1 = 0 - 1

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

Solutions for the range

(0, 2 π)

θ = \frac{3 π}{2}

x, y^{2} = - 2 tan (2 x)

2 cos^{2} (a) - 3 cos (a) + 1 = 0

sin (x) \cdot cos (2 x) = 0.5 - sin (2 x) \cdot cos (x)

tan (x) = 0.625

4 sin^{2} (2 θ) + 6 = 9

What is the general solution for csc(θ)+1=0,(0,2pi) ?
The general solution for csc(θ)+1=0,(0,2pi) is θ=(3pi)/2