What is the value of sin(pi 1/4) ?

The value of sin(pi 1/4) is (sqrt(2))/2

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sin(pi 1/4)

sin (π \frac{1}{4})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (π \frac{1}{4})

Simplify:

π \frac{1}{4} = \frac{π}{4}

π \frac{1}{4}

Multiply fractions:

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

= \frac{1 π}{4}

Multiply:

1 π = π

= \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{2}{2}

sin (2 arctan (- 2))

- 3 cos (2 (\frac{π}{2})) + 3

cos (\frac{π}{5}) cos (\frac{2 π}{5}) cos (\frac{4 π}{5}) cos (\frac{8 π}{5})

8 \cdot sin (1375. 1^{\circ})

sin (\frac{π}{2} - 1)