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

The value of -cot((3pi)/2)csc((3pi)/2) is 0

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

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

0

Solution steps

- cot (\frac{3 π}{2}) csc (\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}) csc (\frac{3 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 \cdot csc (\frac{3 π}{2})

= - 0 \cdot csc (\frac{3 π}{2})

Simplify

= 0

tan (\frac{3}{4} π)

sin (arcsin (0.5))

25 sin (4 0^{\circ})

cot (\frac{11 π}{12})

arcsin (0.86)

What is the value of -cot((3pi)/2)csc((3pi)/2) ?
The value of -cot((3pi)/2)csc((3pi)/2) is 0