What is the value of pi/3 cos(pi/3) ?

The value of pi/3 cos(pi/3) is pi/6

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pi/3 cos(pi/3)

\frac{π}{3} cos (\frac{π}{3})

\frac{π}{6}

Decimal Notation

0.52359 \dots

Solution steps

\frac{π}{3} cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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}

= \frac{1}{2}

= \frac{π}{3} \cdot \frac{1}{2}

Simplify

\frac{π}{3} \cdot \frac{1}{2} : \frac{π}{6}

\frac{π}{3} \cdot \frac{1}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{π 1}{3 \cdot 2}

Multiply:

π 1 = π

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= \frac{π}{6}

\frac{cos ^{2} ( \frac{π}{4} )}{2}

arctan (\frac{6}{17})

29 \cdot cos (- 5.9 1^{\circ})

2 (1)^{2} + 2 arcsin (1)

sin (7 \cdot \frac{π}{2})