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

The value of 1/2 sin(2(pi/2)) is 0

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

\frac{1}{2} sin (2 (\frac{π}{2}))

0

Solution steps

\frac{1}{2} sin (2 (\frac{π}{2}))

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

Rewrite using trig identities:

sin (2 \cdot \frac{π}{2}) = 0

sin (2 \cdot \frac{π}{2})

Simplify:

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 2}{2}

Cancel the common factor:

2

= π

= sin (π)

Use the following trivial identity:

sin (π) = 0

sin (π)

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} \cdot 0

Simplify

= 0

arcsin (\frac{1.5}{2.6})

arccos (22)

arccos (\frac{- 2}{3})

arctan (0.55)

arctan (0.53)