What is the value of 1/4 cos(0) ?

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1/4 cos(0)

\frac{1}{4} cos (0)

\frac{1}{4}

Decimal Notation

0.25

Solution steps

\frac{1}{4} cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{1}{4} \cdot 1

Simplify

= \frac{1}{4}

sin (\frac{2 π}{2}) + cos (\frac{2 π}{2})

cos (5.5)

- 51.875 cos (\frac{2 π}{365} (55 - 354)) + 727.725

(cot (1 0^{\circ}) - cot (8 0^{\circ})) tan (2 0^{\circ})

cos (\frac{17 π}{6}) \cdot sec (- 6 0^{\circ}) + cot (21 0^{\circ})