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

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

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sin(pi/2+pi/2)

sin (\frac{π}{2} + \frac{π}{2})

0

Solution steps

sin (\frac{π}{2} + \frac{π}{2})

Simplify:

\frac{π}{2} + \frac{π}{2} = π

\frac{π}{2} + \frac{π}{2}

Apply rule

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

= \frac{π + π}{2}

Add similar elements:

π + π = 2 π

= \frac{2 π}{2}

Divide the numbers:

\frac{2}{2} = 1

= 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

cos (\frac{11}{122})

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\frac{3}{2} sec (\frac{5 π}{3})

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