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

The value of pi/4*sin(pi/4) is (sqrt(2)pi)/8

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pi/4*sin(pi/4)

\frac{π}{4} \cdot sin (\frac{π}{4})

\frac{2 π}{8}

Decimal Notation

0.55536 \dots

Solution steps

\frac{π}{4} sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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

= \frac{2}{2}

= \frac{π}{4} \cdot \frac{2}{2}

Simplify

\frac{π}{4} \cdot \frac{2}{2} : \frac{2 π}{8}

\frac{π}{4} \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{π 2}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{2 π}{8}

= \frac{2 π}{8}

arcsin (0.17)

sin (27 π)

csc^{2} (4 5^{\circ}) + cot^{2} (3 0^{\circ}) - 2 sec (6 0^{\circ})

cos (2 9^{\circ}) \cdot 46.6

sin (arccos (\frac{3}{7}))

What is the value of pi/4*sin(pi/4) ?
The value of pi/4*sin(pi/4) is (sqrt(2)pi)/8