What is the value of pi*cos(pi/4) ?

The value of pi*cos(pi/4) is (sqrt(2)pi)/2

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pi*cos(pi/4)

π \cdot cos (\frac{π}{4})

\frac{2 π}{2}

Decimal Notation

2.22144 \dots

Solution steps

π cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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{2}{2}

= π \frac{2}{2}

Simplify

π \frac{2}{2} : \frac{2 π}{2}

π \frac{2}{2}

Multiply fractions:

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

= \frac{2 π}{2}

= \frac{2 π}{2}

sin (- \frac{14 π}{3})

\frac{1 + cos ( \frac{5}{13} )}{2}

sin (\frac{6 π}{7}) cos (\frac{11 π}{21}) - cos (\frac{6 π}{7}) sin (\frac{11 π}{21})

7.05 tan (4 2^{\circ})

sin^{2} (2 3^{\circ}) + sin^{2} (6 7^{\circ})