What is the value of cos((pi/3)/2) ?

The value of cos((pi/3)/2) is (sqrt(3))/2

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cos((pi/3)/2)

cos (\frac{\frac{π}{3}}{2})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

cos (\frac{\frac{π}{3}}{2})

Simplify:

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= \frac{3}{2}

5 cos (\frac{7 π}{6})

arctan (- \frac{7}{5})

- \frac{1}{cos ( \frac{π}{4} )}

sin (2 \cdot 2 π)

sin (3 5^{\circ}) cos (2 5^{\circ}) + cos (3 5^{\circ}) sin (2 5^{\circ})