What is the value of arcsin(tan(45)) ?

The value of arcsin(tan(45)) is pi/2

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arcsin(tan(45))

arcsin (tan (4 5^{\circ}))

\frac{π}{2}

Decimal Notation

90

Solution steps

arcsin (tan (4 5^{\circ}))

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= arcsin (1)

= arcsin (1)

Use the following trivial identity:

arcsin (1) = 9 0^{\circ}

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}

= 9 0^{\circ}

= 9 0^{\circ}

arcsin (0.82)

arcsin (0.78)

arcsin (0.76)

arcsin (0.32)

\frac{tan ( π )}{3}