What is the value of arccos(cos(90)) ?

The value of arccos(cos(90)) is pi/2

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arccos(cos(90))

arccos (cos (9 0^{\circ}))

\frac{π}{2}

Decimal Notation

90

Solution steps

arccos (cos (9 0^{\circ}))

Use the following trivial identity:

cos (9 0^{\circ}) = 0

cos (9 0^{\circ})

cos (x)

periodicity table with

36 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= arccos (0)

= arccos (0)

Use the following trivial identity:

arccos (0) = 9 0^{\circ}

arccos (0)

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 9 0^{\circ}

= 9 0^{\circ}

\frac{12}{cos ( 5 3 ^{\circ} )}

sin (arcsin (\frac{4}{5}))

\frac{π cos ( π ) - sin ( π )}{- π sin ( π ) - cos ( π )}

2 tan (\frac{π}{2})

sin (3 0^{\circ}) + sin (6 0^{\circ})