What is the value of cot(30)-sin(45) ?

The value of cot(30)-sin(45) is sqrt(3)-(sqrt(2))/2

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cot(30)-sin(45)

cot (3 0^{\circ}) - sin (4 5^{\circ})

3 - \frac{2}{2}

Decimal Notation

1.02494 \dots

Solution steps

cot (3 0^{\circ}) - sin (4 5^{\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

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

periodicity table with

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= 3 - \frac{2}{2}

cos (2.2)

sec^{2} (4 0^{\circ})

tan (\frac{π}{4}) - tan (\frac{π}{6})

sec (25 0^{\circ})

cot^{2} (\frac{1}{2})

What is the value of cot(30)-sin(45) ?
The value of cot(30)-sin(45) is sqrt(3)-(sqrt(2))/2