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

The value of arcsin(csc(pi/2)) is pi/2

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arcsin(csc(pi/2))

arcsin (csc (\frac{π}{2}))

\frac{π}{2}

Decimal Notation

90

Solution steps

arcsin (csc (\frac{π}{2}))

Use the following trivial identity:

csc (\frac{π}{2}) = 1

csc (\frac{π}{2})

csc (x)

periodicity table with

2 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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= arcsin (1)

= arcsin (1)

Use the following trivial identity:

arcsin (1) = \frac{π}{2}

arcsin (1)

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}

= \frac{π}{2}

= \frac{π}{2}

cos (\frac{4 π}{7})

121 sin (4 5^{\circ})

sin (e^{- 1})

5 arctan (6) - 6

\frac{tan ( 4 ( 0.1 ) )}{tan ( 5 ( 0.1 ) )}