What is the value of 3csc(3((2pi)/9)) ?

The value of 3csc(3((2pi)/9)) is 2sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3csc(3((2pi)/9))

3 csc (3 (\frac{2 π}{9}))

23

Decimal Notation

3.46410 \dots

Solution steps

3 csc (3 (\frac{2 π}{9}))

= 3 csc (3 \cdot \frac{2 π}{9})

Simplify:

3 \cdot \frac{2 π}{9} = \frac{2 π}{3}

3 \cdot \frac{2 π}{9}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 π 3}{9}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{6 π}{9}

Cancel the common factor:

3

= \frac{2 π}{3}

= 3 csc (\frac{2 π}{3})

Rewrite using trig identities:

csc (\frac{2 π}{3}) = \frac{2 3}{3}

csc (\frac{2 π}{3})

Rewrite using trig identities:

\frac{1}{sin ( \frac{2 π}{3} )}

csc (\frac{2 π}{3})

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( \frac{2 π}{3} )}

= \frac{1}{sin ( \frac{2 π}{3} )}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

sin (\frac{2 π}{3})

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

= \frac{3}{2}

= \frac{1}{\frac{3}{2}}

Simplify

\frac{1}{\frac{3}{2}} : \frac{2 3}{3}

\frac{1}{\frac{3}{2}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2}{3}

Rationalize

\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}

= \frac{2 3}{3}

= \frac{2 3}{3}

= 3 \cdot \frac{2 3}{3}

Simplify

3 \cdot \frac{2 3}{3} : 23

3 \cdot \frac{2 3}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 3 \cdot 3}{3}

Cancel the common factor:

3

= 23

= 23

sin (2 π) - sin (π)

sin (13 5^{\circ}) + cos (13 5^{\circ}) + tan (13 5^{\circ})

tan (arcsin (\frac{- 12}{13}))

sec (- 84 0^{\circ})

sec (arccos (- \frac{3}{5}))

What is the value of 3csc(3((2pi)/9)) ?
The value of 3csc(3((2pi)/9)) is 2sqrt(3)