What is the value of cot(780) ?

The value of cot(780) is (sqrt(3))/3

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cot(780)

cot (78 0^{\circ})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

cot (78 0^{\circ})

cot (78 0^{\circ}) = cot (6 0^{\circ})

cot (78 0^{\circ})

Rewrite

78 0^{\circ}

18 0^{\circ} \cdot 4 + 6 0^{\circ}

= cot (18 0^{\circ} 4 + 6 0^{\circ})

Apply the periodicity of

cot

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

cot (18 0^{\circ} \cdot 4 + 6 0^{\circ}) = cot (6 0^{\circ})

= cot (6 0^{\circ})

= 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}

= \frac{3}{3}

arctan (\frac{5 π}{2})

\frac{sin ( 1 7 ^{\circ} ) cos ( 1 3 ^{\circ} ) + sin ( 1 3 ^{\circ} ) cos ( 1 7 ^{\circ} )}{cos ( 2 6 ^{\circ} ) cos ( 1 9 ^{\circ} ) - sin ( 2 6 ^{\circ} ) sin ( 1 9 ^{\circ} )}

sin (4 2^{\circ}) cos (1 2^{\circ}) - cos (4 2^{\circ}) sin (1 2^{\circ})

9.81 \cdot cos (3 0^{\circ})

50 arcsin (\frac{21}{5}) - 421