What is the general solution for 2=-4-3csc(θ) ?

The general solution for 2=-4-3csc(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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2=-4-3csc(θ)

2 = - 4 - 3 csc (θ)

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 21 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

2 = - 4 - 3 csc (θ)

Switch sides

- 4 - 3 csc (θ) = 2

Move

4

to the right side

- 4 - 3 csc (θ) = 2

Add

4

to both sides

- 4 - 3 csc (θ) + 4 = 2 + 4

Simplify

- 3 csc (θ) = 6

- 3 csc (θ) = 6

Divide both sides by

- 3

- 3 csc (θ) = 6

Divide both sides by

- 3

\frac{- 3 csc ( θ )}{- 3} = \frac{6}{- 3}

Simplify

\frac{- 3 csc ( θ )}{- 3} = \frac{6}{- 3}

Simplify

\frac{- 3 csc ( θ )}{- 3} : csc (θ)

\frac{- 3 csc ( θ )}{- 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 csc ( θ )}{3}

Divide the numbers:

\frac{3}{3} = 1

= csc (θ)

Simplify

\frac{6}{- 3} : - 2

\frac{6}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= - 2

csc (θ) = - 2

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{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

x, 3 tan (2 x) = - 1

1 + sin^{2} (x) = 0

2 sin^{2} (x) + 4 cos^{2} (x) = 1

- sin (θ) = \frac{n}{2} - 3

3 sin (θ) + 2 sin^{2} (θ) = - 1, 0 \leq θ < 2 π

What is the general solution for 2=-4-3csc(θ) ?
The general solution for 2=-4-3csc(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin