What is the value of cot((3pi)/2)-cot(pi/6) ?

The value of cot((3pi)/2)-cot(pi/6) is -sqrt(3)

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cot((3pi)/2)-cot(pi/6)

cot (\frac{3 π}{2}) - cot (\frac{π}{6})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

cot (\frac{3 π}{2}) - cot (\frac{π}{6})

Rewrite using trig identities:

cot (\frac{3 π}{2}) = 0

cot (\frac{3 π}{2})

cot (\frac{3 π}{2}) = cot (\frac{π}{2})

cot (\frac{3 π}{2})

Rewrite

\frac{3 π}{2}

π + \frac{π}{2}

= cot (π + \frac{π}{2})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \frac{π}{2}) = cot (\frac{π}{2})

= cot (\frac{π}{2})

= cot (\frac{π}{2})

Use the following trivial identity:

cot (\frac{π}{2}) = 0

cot (\frac{π}{2})

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 0

= 0

Use the following trivial identity:

cot (\frac{π}{6}) = 3

cot (\frac{π}{6})

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 3

= 0 - 3

Simplify

= - 3

arctan (0.85)

30 sin (1 5^{\circ})

2 sin (2 6^{\circ}) cos (2 6^{\circ})

arctan (0.78)

arctan (3) - arctan (- 3)

What is the value of cot((3pi)/2)-cot(pi/6) ?
The value of cot((3pi)/2)-cot(pi/6) is -sqrt(3)