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

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

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sin(pi/2+pi)

sin (\frac{π}{2} + π)

- 1

Solution steps

sin (\frac{π}{2} + π)

Rewrite using trig identities:

sin (π) cos (\frac{π}{2}) + cos (π) sin (\frac{π}{2})

= sin (π) cos (\frac{π}{2}) + cos (π) sin (\frac{π}{2})

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{2}) = 1

= 0 \cdot 0 + (- 1) \cdot 1

Simplify

= - 1

2 sec (- \frac{π}{3})

cos (\frac{π}{6}) cos (\frac{π}{3}) - sin (\frac{π}{6}) sin (\frac{π}{3})

100 sin (9 0^{\circ})

cos^{2} (\frac{π}{6}) - 2 sin (\frac{π}{6})

arctan (\frac{7.7}{14})