What is the value of arccos(sec(pi)) ?

The value of arccos(sec(pi)) is pi

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arccos(sec(pi))

arccos (sec (π))

π

Decimal Notation

180

Solution steps

arccos (sec (π))

Use the following trivial identity:

sec (π) = (- 1)

sec (π)

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= arccos (- 1)

= arccos (- 1)

Use the following trivial identity:

arccos (- 1) = π

arccos (- 1)

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}

= π

= π

cos (arctan (\frac{2}{3}) - arccos (\frac{3}{5}))

tan (13 5^{\circ} - 4 5^{\circ})

cos (4 arctan (2))

2 arccos (\frac{1}{2})

sin (arccos (\frac{8}{10}) + arctan (- \frac{6}{8}))