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

The general solution for 2csc(θ)+3=0 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin

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2csc(θ)+3=0

2 csc (θ) + 3 = 0

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

Degrees

θ = - 41.81031 \dots^{\circ} + 36 0^{\circ} n, θ = 221.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 csc (θ) + 3 = 0

Move

3

to the right side

2 csc (θ) + 3 = 0

Subtract

3

from both sides

2 csc (θ) + 3 - 3 = 0 - 3

Simplify

2 csc (θ) = - 3

2 csc (θ) = - 3

Divide both sides by

2

2 csc (θ) = - 3

Divide both sides by

2

\frac{2 csc ( θ )}{2} = \frac{- 3}{2}

Simplify

csc (θ) = - \frac{3}{2}

csc (θ) = - \frac{3}{2}

Apply trig inverse properties

csc (θ) = - \frac{3}{2}

General solutions for

csc (θ) = - \frac{3}{2}

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

θ = arccsc (- \frac{3}{2}) + 2 πn, θ = π + arccsc (\frac{3}{2}) + 2 πn

θ = arccsc (- \frac{3}{2}) + 2 πn, θ = π + arccsc (\frac{3}{2}) + 2 πn

Show solutions in decimal form

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

2 cos (x) - 2 sin (2 x) = 0

cos (x) + 3 sin (x) = 1

2 sin^{2} (x) = 4 sin (x) + 6

cos (x) = sin (1 5^{\circ})

3 = 3 tan (x)

What is the general solution for 2csc(θ)+3=0 ?
The general solution for 2csc(θ)+3=0 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin