What is the value of arcsin(tan((5pi)/4)) ?

The value of arcsin(tan((5pi)/4)) is pi/2

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arcsin(tan((5pi)/4))

arcsin (tan (\frac{5 π}{4}))

\frac{π}{2}

Decimal Notation

90

Solution steps

arcsin (tan (\frac{5 π}{4}))

Rewrite using trig identities:

tan (\frac{5 π}{4}) = 1

tan (\frac{5 π}{4})

tan (\frac{5 π}{4}) = tan (\frac{π}{4})

tan (\frac{5 π}{4})

Rewrite

\frac{5 π}{4}

π + \frac{π}{4}

= tan (π + \frac{π}{4})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{π}{4}) = tan (\frac{π}{4})

= tan (\frac{π}{4})

= tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 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}

ln ∣ sinh (1) ∣

cos (18.1 9^{\circ})

\frac{1}{2} sin (2) (\frac{π}{2})

2 - 2 cos (\frac{π}{2})

arctan (- 473)

What is the value of arcsin(tan((5pi)/4)) ?
The value of arcsin(tan((5pi)/4)) is pi/2