What is the general solution for csc(θ)=-2/(sqrt(3)) ?

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

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csc(θ)=-2/(sqrt(3))

csc (θ) = - \frac{2}{3}

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

csc (θ) = - \frac{2}{3}

Simplify

- \frac{2}{3} : - \frac{2 3}{3}

- \frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

csc (θ) = - \frac{2 3}{3}

General solutions for

csc (θ) = - \frac{2 3}{3}

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{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

2 cos (\frac{x}{2}) + 3 = 0

\frac{1}{cos ( x )} = - 2

25 sin (x) cos (x) - 5 sin (x) + 20 cos (x) = 4

sin (θ) = - 0.9

cos (2 T) = 1, 0 \leq T \leq 2 π

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