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

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

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1/2 sin(2*pi/4)

\frac{1}{2} sin (2 \cdot \frac{π}{4})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\frac{1}{2} sin (2 \cdot \frac{π}{4})

Rewrite using trig identities:

sin (2 \cdot \frac{π}{4}) = 1

sin (2 \cdot \frac{π}{4})

Simplify:

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 1

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

Simplify

= \frac{1}{2}

arccos (cos (\frac{- π}{6}))

sin (28.0 7^{\circ})

5 cos (54 0^{\circ})

csc (0.9)

arcsin (\frac{12}{11} sin (7 3^{\circ}))