What is the value of (cos((11pi)/6))/(sin((11pi)/6)) ?

The value of (cos((11pi)/6))/(sin((11pi)/6)) is -sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos((11pi)/6))/(sin((11pi)/6))

\frac{cos ( \frac{11 π}{6} )}{sin ( \frac{11 π}{6} )}

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

\frac{cos ( \frac{11 π}{6} )}{sin ( \frac{11 π}{6} )}

Rewrite using trig identities:

cot (\frac{5 π}{6})

\frac{cos ( \frac{11 π}{6} )}{sin ( \frac{11 π}{6} )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (\frac{11 π}{6})

cot (\frac{11 π}{6}) = cot (\frac{5 π}{6})

cot (\frac{11 π}{6})

Rewrite

\frac{11 π}{6}

π + \frac{5 π}{6}

= cot (π + \frac{5 π}{6})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \frac{5 π}{6}) = cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

Use the following trivial identity:

cot (\frac{5 π}{6}) = - 3

cot (\frac{5 π}{6})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= - 3

= - 3

3 + 2 sin (\frac{3 π}{2})

12.4 - 10 (0.5 π - arcsin (0.5) - 0.5 (1 - (0.5)^{2})^{\frac{1}{2}})

sin (\frac{11}{9}) π

\frac{1.24}{tan ( 3 4 ^{\circ} )}

\frac{sin ( 3 0 ^{\circ} )}{sin ( 2 2 ^{\circ} )}

What is the value of (cos((11pi)/6))/(sin((11pi)/6)) ?
The value of (cos((11pi)/6))/(sin((11pi)/6)) is -sqrt(3)