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

The value of arccos(cot(pi/4)) is 0

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arccos(cot(pi/4))

arccos (cot (\frac{π}{4}))

0

Solution steps

arccos (cot (\frac{π}{4}))

Use the following trivial identity:

cot (\frac{π}{4}) = 1

cot (\frac{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

= arccos (1)

= arccos (1)

Use the following trivial identity:

arccos (1) = 0

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}

= 0

= 0

- 2 sin^{3} (0) cos (0) + 3 \cdot 0 - \frac{3}{2} sin (0)

arctan (\frac{3.3}{9.8} + 0.4)

sin (12 9^{\circ})

3 + 2 sin (- \frac{π}{3})

arccos (\frac{24}{46 59})