What is the general solution for 5csc(θ)+6=0 ?

The general solution for 5csc(θ)+6=0 is θ=-0.98511…+2pin,θ=pi+0.98511…+2pin

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5csc(θ)+6=0

5 csc (θ) + 6 = 0

θ = - 0.98511 \dots + 2 πn, θ = π + 0.98511 \dots + 2 πn

Solution steps

5 csc (θ) + 6 = 0

Move

6

to the right side

5 csc (θ) = - 6

Divide both sides by

5

csc (θ) = - \frac{6}{5}

Apply trig inverse properties

θ = arccsc (- \frac{6}{5}) + 2 πn, θ = π + arccsc (\frac{6}{5}) + 2 πn

Show solutions in decimal form

θ = - 0.98511 \dots + 2 πn, θ = π + 0.98511 \dots + 2 πn

sin (x^{2}) = 1

cos (2 θ) - 3 cos (θ) = 0, 0 \leq θ < 2 π

2 cos^{2} (θ) - 7 cos (θ) - 4 = 0

sin (θ) = \frac{3}{10}, sin (θ + \frac{π}{6})

3 sin^{2} (x) = 8 cos (x)

What is the general solution for 5csc(θ)+6=0 ?
The general solution for 5csc(θ)+6=0 is θ=-0.98511…+2pin,θ=pi+0.98511…+2pin