What is (e^{5i}-e^{-5i})/(2i) ?

The solution to (e^{5i}-e^{-5i})/(2i) is sin(5)

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simplify (e^{5i}-e^{-5i})/(2i)

simplify

\frac{e ^{5 i} - e ^{- 5 i}}{2 i}

sin (5)

Solution steps

\frac{e ^{5 i} - e ^{- 5 i}}{2 i}

e^{5 i} - e^{- 5 i} = cos (5) + i sin (5) - (cos (5) - i sin (5))

= \frac{cos ( 5 ) + i sin ( 5 ) - ( - i sin ( 5 ) + cos ( 5 ) )}{2 i}

Expand

cos (5) + sin (5) i - (cos (5) - sin (5) i) : 2 i sin (5)

= \frac{2 i sin ( 5 )}{2 i}

Divide the numbers:

\frac{2}{2} = 1

= \frac{i sin ( 5 )}{i}

Cancel the common factor:

i

= sin (5)

- 4 x - 23 \geq 2 - 3 (3 + 2 x)

g^{2} + 7 g = 144

2 (\frac{3}{5}) (\frac{4}{5})

m^{2} - 8 m + 16

\frac{1}{4} (- 2) (- 4) (- 7) (- 9)