What is the general solution for sqrt(3csc(x))=2 ?

The general solution for sqrt(3csc(x))=2 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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sqrt(3csc(x))=2

3 csc (x) = 2

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

3 csc (x) = 2

Square both sides:

3 csc (x) = 4

3 csc (x) = 4

Solve

3 csc (x) = 4 : csc (x) = \frac{4}{3}

csc (x) = \frac{4}{3}

Verify Solutions:

csc (x) = \frac{4}{3}

True

The solution is

csc (x) = \frac{4}{3}

Apply trig inverse properties

x = arccsc (\frac{4}{3}) + 2 πn, x = π - arccsc (\frac{4}{3}) + 2 πn

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

4 csc^{2} (x) - 25 = 0

sin (θ) = - \frac{4}{5}, \frac{3 π}{2} < θ < 2 π

4 cos (x) + sin^{2} (x) = 3 cos^{2} (x) + 2

5 tan (B) + 13 = 0

tan^{2} (x) = 3 tan (x)

What is the general solution for sqrt(3csc(x))=2 ?
The general solution for sqrt(3csc(x))=2 is x=0.84806…+2pin,x=pi-0.84806…+2pin