What is the value of 80cot(60) ?

The value of 80cot(60) is (80sqrt(3))/3

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80cot(60)

80 cot (6 0^{\circ})

\frac{80 3}{3}

Decimal Notation

46.18802 \dots

Solution steps

80 cot (6 0^{\circ})

Use the following trivial identity:

cot (6 0^{\circ}) = \frac{3}{3}

cot (6 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}

= 80 \cdot \frac{3}{3}

Simplify

80 \cdot \frac{3}{3} : \frac{80 3}{3}

80 \cdot \frac{3}{3}

Multiply fractions:

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

= \frac{3 \cdot 80}{3}

Apply radical rule:

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

= \frac{80 \cdot 3 ^{\frac{1}{2}}}{3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{80}{3 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{80}{3 ^{\frac{1}{2}}}

Apply radical rule:

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

= \frac{80}{3}

Rationalize

\frac{80}{3} : \frac{80 3}{3}

\frac{80}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{80 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{80 3}{3}

= \frac{80 3}{3}

= \frac{80 3}{3}

75 0^{2} + 90 0^{2} - 2 \cdot 750 \cdot 900 \cdot [cos (9 5^{\circ})]

cos (- 6 0^{\circ}) - tan (- 4 5^{\circ})

cos (arccos (\frac{2}{7}))

cos (arccot (2) + arccot (3))

arctan (\frac{2 3}{3})