What is the general solution for 3csc(θ)+5=0 ?

The general solution for 3csc(θ)+5=0 is θ=-0.64350…+2pin,θ=pi+0.64350…+2pin

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3csc(θ)+5=0

3 csc (θ) + 5 = 0

θ = - 0.64350 \dots + 2 πn, θ = π + 0.64350 \dots + 2 πn

Degrees

θ = - 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 216.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 csc (θ) + 5 = 0

Move

5

to the right side

3 csc (θ) + 5 = 0

Subtract

5

from both sides

3 csc (θ) + 5 - 5 = 0 - 5

Simplify

3 csc (θ) = - 5

3 csc (θ) = - 5

Divide both sides by

3

3 csc (θ) = - 5

Divide both sides by

3

\frac{3 csc ( θ )}{3} = \frac{- 5}{3}

Simplify

csc (θ) = - \frac{5}{3}

csc (θ) = - \frac{5}{3}

Apply trig inverse properties

csc (θ) = - \frac{5}{3}

General solutions for

csc (θ) = - \frac{5}{3}

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

θ = arccsc (- \frac{5}{3}) + 2 πn, θ = π + arccsc (\frac{5}{3}) + 2 πn

θ = arccsc (- \frac{5}{3}) + 2 πn, θ = π + arccsc (\frac{5}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.64350 \dots + 2 πn, θ = π + 0.64350 \dots + 2 πn

cos (\frac{x}{3}) - cos (\frac{x}{15}) = 0

(2 cos (x) - 3) (2 sin (x) + 1) = 0

y, x = π - arcsin (y)

arctan (x) = 3

tan (x) cos (x) = cos (x)

What is the general solution for 3csc(θ)+5=0 ?
The general solution for 3csc(θ)+5=0 is θ=-0.64350…+2pin,θ=pi+0.64350…+2pin