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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)csc(θ)=2

3 csc (θ) = 2

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) = 2

Divide both sides by

3

3 csc (θ) = 2

Divide both sides by

3

\frac{3 csc ( θ )}{3} = \frac{2}{3}

Simplify

\frac{3 csc ( θ )}{3} = \frac{2}{3}

Simplify

\frac{3 csc ( θ )}{3} : csc (θ)

\frac{3 csc ( θ )}{3}

Cancel the common factor:

3

= csc (θ)

Simplify

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

csc (θ) = \frac{2 3}{3}

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

4 sin (x) + 8 = 8

2 cos^{2} (t) - 8 sin^{2} (t) cos (t) - 1 = 0

sin (B) = \frac{4}{5}

cos (2 x) = - 3 cos (x) - 2, 0 < x \leq 2 π

cos (θ) = - \frac{7}{6}

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