What is the general solution for 4csc(x)+5=0 ?

The general solution for 4csc(x)+5=0 is x=-0.92729…+2pin,x=pi+0.92729…+2pin

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4csc(x)+5=0

4 csc (x) + 5 = 0

x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

Degrees

x = - 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 233.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4 csc (x) + 5 = 0

Move

5

to the right side

4 csc (x) + 5 = 0

Subtract

5

from both sides

4 csc (x) + 5 - 5 = 0 - 5

Simplify

4 csc (x) = - 5

4 csc (x) = - 5

Divide both sides by

4

4 csc (x) = - 5

Divide both sides by

4

\frac{4 csc ( x )}{4} = \frac{- 5}{4}

Simplify

csc (x) = - \frac{5}{4}

csc (x) = - \frac{5}{4}

Apply trig inverse properties

csc (x) = - \frac{5}{4}

General solutions for

csc (x) = - \frac{5}{4}

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

x = arccsc (- \frac{5}{4}) + 2 πn, x = π + arccsc (\frac{5}{4}) + 2 πn

x = arccsc (- \frac{5}{4}) + 2 πn, x = π + arccsc (\frac{5}{4}) + 2 πn

Show solutions in decimal form

x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

2 cos (\frac{2 x}{3}) - 1 = 0

tan (x) + 1 = 0, 0 \leq x \leq 2 π

8 sin^{2} (θ) + 10 sin (θ) - 2 = 4 sin (θ) - 3

tan (x) = - \frac{5}{2}

5 sin^{2} (θ) - 4 cos (θ) - 9 = - cos (θ) - 6

What is the general solution for 4csc(x)+5=0 ?
The general solution for 4csc(x)+5=0 is x=-0.92729…+2pin,x=pi+0.92729…+2pin