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

The value of 1/2 (pi-1/2 sin(2pi)) is pi/2

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

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

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

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

Rewrite using trig identities:

sin (2 π) = 0

sin (2 π)

sin (2 π) = sin (0)

sin (2 π)

Rewrite

2 π

2 π + 0

= sin (2 π + 0)

Apply the periodicity of

sin

sin (x + 2 π) = sin (x)

sin (2 π + 0) = sin (0)

= sin (0)

= sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

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}

= 0

= 0

= \frac{1}{2} (π - \frac{1}{2} \cdot 0)

Simplify

\frac{1}{2} (π - \frac{1}{2} \cdot 0) : \frac{π}{2}

\frac{1}{2} (π - \frac{1}{2} \cdot 0)

Apply rule

0 \cdot a = 0

= \frac{1}{2} (π - 0)

π - 0 = π

= π \frac{1}{2}

Multiply fractions:

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

= \frac{1 π}{2}

Multiply:

1 π = π

= \frac{π}{2}

= \frac{π}{2}

cos (arcsin (\frac{1}{5}) + arctan (\frac{1}{3}))

sin (arcsin (\frac{5}{13}) + arccos (- \frac{3}{5}))

sin (\frac{π}{2}) - 2

4 sin (\frac{11 π}{6})

\frac{6}{cos ( 3 7 ^{\circ} )}

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