What is the general solution for 3csc(θ)-2sqrt(3)=0 ?

The general solution for 3csc(θ)-2sqrt(3)=0 is θ= pi/3+2pin,θ=(2pi)/3+2pin

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3csc(θ)-2sqrt(3)=0

3 csc (θ) - 23 = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

Degrees

θ = 6 0^{\circ} + 36 0^{\circ} n, θ = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

3 csc (θ) - 23 = 0

Move

23

to the right side

3 csc (θ) - 23 = 0

Add

23

to both sides

3 csc (θ) - 23 + 23 = 0 + 23

Simplify

3 csc (θ) = 23

3 csc (θ) = 23

Divide both sides by

3

3 csc (θ) = 23

Divide both sides by

3

\frac{3 csc ( θ )}{3} = \frac{2 3}{3}

Simplify

csc (θ) = \frac{2 3}{3}

csc (θ) = \frac{2 3}{3}

General solutions for

csc (θ) = \frac{2 3}{3}

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

(sin (x) + 2) (2 sin (x) + 1) = 0

5 sin (2 θ) = - \frac{1}{5}

sin (θ) = \frac{8}{17}, cos (θ) = \frac{15}{17}, tan (θ)

\frac{1}{sin ^{2} ( x )} = \frac{1}{cos ^{2} ( x )}

sin (θ) = - \frac{12}{13}, sec (θ)

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