What is the general solution for (csc(x))/5-2=0 ?

The general solution for (csc(x))/5-2=0 is x=0.10016…+2pin,x=pi-0.10016…+2pin

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(csc(x))/5-2=0

\frac{csc ( x )}{5} - 2 = 0

x = 0.10016 \dots + 2 πn, x = π - 0.10016 \dots + 2 πn

Degrees

x = 5.73917 \dots^{\circ} + 36 0^{\circ} n, x = 174.26082 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{csc ( x )}{5} - 2 = 0

Move

2

to the right side

\frac{csc ( x )}{5} - 2 = 0

Add

2

to both sides

\frac{csc ( x )}{5} - 2 + 2 = 0 + 2

Simplify

\frac{csc ( x )}{5} = 2

\frac{csc ( x )}{5} = 2

Multiply both sides by

5

\frac{csc ( x )}{5} = 2

Multiply both sides by

5

\frac{5 csc ( x )}{5} = 2 \cdot 5

Simplify

csc (x) = 10

csc (x) = 10

Apply trig inverse properties

csc (x) = 10

General solutions for

csc (x) = 10

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

x = arccsc (10) + 2 πn, x = π - arccsc (10) + 2 πn

x = arccsc (10) + 2 πn, x = π - arccsc (10) + 2 πn

Show solutions in decimal form

x = 0.10016 \dots + 2 πn, x = π - 0.10016 \dots + 2 πn

What is the general solution for (csc(x))/5-2=0 ?
The general solution for (csc(x))/5-2=0 is x=0.10016…+2pin,x=pi-0.10016…+2pin