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

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

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(sin(pi/4))/(pi/4)

\frac{sin ( \frac{π}{4} )}{\frac{π}{4}}

\frac{2 2}{π}

Decimal Notation

0.90031 \dots

Solution steps

\frac{sin ( \frac{π}{4} )}{\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{\frac{2}{2}}{\frac{π}{4}}

Simplify

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

\frac{\frac{2}{2}}{\frac{π}{4}}

Divide fractions:

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

= \frac{2 \cdot 4}{2 π}

Divide the numbers:

\frac{4}{2} = 2

= \frac{2 2}{π}

= \frac{2 2}{π}

arctan (\frac{- 5}{4})

arctan (\frac{6}{13})

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

sin (\frac{1}{( \frac{2}{π} )})

cos (- \frac{2}{3} π)

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