What is the value of 1/(cot(330)) ?

The value of 1/(cot(330)) is -(sqrt(3))/3

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1/(cot(330))

\frac{1}{cot ( 33 0 ^{\circ} )}

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

\frac{1}{cot ( 33 0 ^{\circ} )}

Rewrite using trig identities:

cot (33 0^{\circ}) = - 3

cot (33 0^{\circ})

cot (33 0^{\circ}) = cot (15 0^{\circ})

cot (33 0^{\circ})

Rewrite

33 0^{\circ}

18 0^{\circ} + 15 0^{\circ}

= cot (18 0^{\circ} + 15 0^{\circ})

Apply the periodicity of

cot

cot (x + 18 0^{\circ}) = cot (x)

cot (18 0^{\circ} + 15 0^{\circ}) = cot (15 0^{\circ})

= cot (15 0^{\circ})

= cot (15 0^{\circ})

Use the following trivial identity:

cot (15 0^{\circ}) = - 3

cot (15 0^{\circ})

cot (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= - 3

= - 3

= \frac{1}{- 3}

Simplify

\frac{1}{- 3} : - \frac{3}{3}

\frac{1}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

= - \frac{3}{3}

arctan (\frac{26000}{40000})

arctan (- \frac{4}{- 4})

(30)^{2} + (20)^{2} - 2 (30) (20) cos (106.9 7^{\circ})

128 + 127.5 sin (\frac{2 π}{16} \cdot 1)

- 5 sin (\frac{π}{4})