What is the value of arcsin(cot((3pi)/4)) ?

The value of arcsin(cot((3pi)/4)) is -pi/2

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arcsin(cot((3pi)/4))

arcsin (cot (\frac{3 π}{4}))

- \frac{π}{2}

Decimal Notation

- 90

Solution steps

arcsin (cot (\frac{3 π}{4}))

Use the following trivial identity:

cot (\frac{3 π}{4}) = - 1

cot (\frac{3 π}{4})

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 (- 1)

= arcsin (- 1)

Rewrite using trig identities:

arcsin (- 1) = - \frac{π}{2}

arcsin (- 1)

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- 1) = - 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{π}{2}

cos (\frac{2 π}{9})

\frac{tan ( 1 5 ^{\circ} ) + tan ( 1 5 ^{\circ} )}{1 - tan ( 1 5 ^{\circ} ) tan ( 1 5 ^{\circ} )}

arctan (\frac{- 2 3}{2})

cos (\frac{4}{7})

cos^{2} (31 5^{\circ})

What is the value of arcsin(cot((3pi)/4)) ?
The value of arcsin(cot((3pi)/4)) is -pi/2