What is the value of cot(750) ?

The value of cot(750) is square root of 3

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cot(750)

cot (75 0^{\circ})

3

Decimal Notation

1.73205 \dots

Solution steps

cot (75 0^{\circ})

cot (75 0^{\circ}) = cot (3 0^{\circ})

cot (75 0^{\circ})

Rewrite

75 0^{\circ}

18 0^{\circ} \cdot 4 + 3 0^{\circ}

= cot (18 0^{\circ} 4 + 3 0^{\circ})

Apply the periodicity of

cot

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

cot (18 0^{\circ} \cdot 4 + 3 0^{\circ}) = cot (3 0^{\circ})

= cot (3 0^{\circ})

= cot (3 0^{\circ})

Use the following trivial identity:

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

cot (3 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

cos^{2} (4 0^{\circ}) - sin^{2} (4 0^{\circ})

arctan (tan (- \frac{2 π}{3}))

cos (\frac{13 π}{2})

sin (\frac{3 π}{10})

12 \cdot sin (3 0^{\circ})