What is the value of arcsin(cot(pi/2)) ?

The value of arcsin(cot(pi/2)) is 0

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arcsin(cot(pi/2))

arcsin (cot (\frac{π}{2}))

0

Solution steps

arcsin (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

= arcsin (0)

= arcsin (0)

Use the following trivial identity:

arcsin (0) = 0

arcsin (0)

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0

= 0