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 property:

csc (- x) = - csc (x)

csc (- \frac{π}{2}) = - csc (\frac{π}{2})

= arcsin (- csc (\frac{π}{2}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- csc (\frac{π}{2})) = - arcsin (csc (\frac{π}{2}))

= - 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}

\frac{arctan ( 0 )}{1}

arctan (\frac{0.08}{0.06})

\frac{( 325 \cdot cos ( 2 π \cdot 50 ) ) ^{2}}{10}

sin^{2} (- 9 0^{\circ})

400 cos (2 5^{\circ}) + 700 cos (8 0^{\circ})

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