What is the value of 1/2 sin(1/2 pi/2) ?

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

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1/2 sin(1/2 pi/2)

\frac{1}{2} sin (\frac{1}{2} \frac{π}{2})

\frac{2}{4}

Decimal Notation

0.35355 \dots

Solution steps

\frac{1}{2} sin (\frac{1}{2} \cdot \frac{π}{2})

Simplify:

\frac{1}{2} \cdot \frac{π}{2} = \frac{π}{4}

\frac{1}{2} \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{1 π}{2 \cdot 2}

Multiply:

1 π = π

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{1}{2} sin (\frac{π}{4}) = \frac{sin ( \frac{π}{4} )}{2}

\frac{1}{2} sin (\frac{π}{4})

Multiply fractions:

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

= \frac{1 \cdot sin ( \frac{π}{4} )}{2}

Multiply:

1 \cdot sin (\frac{π}{4}) = sin (\frac{π}{4})

= \frac{sin ( \frac{π}{4} )}{2}

= \frac{sin ( \frac{π}{4} )}{2}

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}}{2}

Simplify

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

\frac{\frac{2}{2}}{2}

Apply the fraction rule:

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

= \frac{2}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{2}{4}

cos (- 8) 43

\frac{30}{18.51 cos ( 3 5 ^{\circ} )}

1 - 2 sec (0)

14 [cos (\frac{π}{2}) + i sin (\frac{π}{2})]

arctan (- \frac{11}{15})

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