What is the value of cot(300) ?

The value of cot(300) is -(sqrt(3))/3

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cot(300)

cot (30 0^{\circ})

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

cot (30 0^{\circ})

cot (30 0^{\circ}) = cot (12 0^{\circ})

cot (30 0^{\circ})

Rewrite

30 0^{\circ}

18 0^{\circ} + 12 0^{\circ}

= cot (18 0^{\circ} + 12 0^{\circ})

Apply the periodicity of

cot

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

cot (18 0^{\circ} + 12 0^{\circ}) = cot (12 0^{\circ})

= cot (12 0^{\circ})

= cot (12 0^{\circ})

Use the following trivial identity:

cot (12 0^{\circ}) = - \frac{3}{3}

cot (12 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

= - \frac{3}{3}

= - \frac{3}{3}

tan (- 6 0^{\circ})

sinh (2)

tan (- 3 0^{\circ})

arccsc (1)

sin^{2} (2)