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

The value of sin(pi+i*pi/2) is i(1-e^pi)/(2e^{pi/2)}

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sin(pi+i*pi/2)

sin (π + i \cdot \frac{π}{2})

i \frac{1 - e ^{π}}{2 e ^{\frac{π}{2}}}

Solution steps

sin (π + i \frac{π}{2})

Rewrite using trig identities:

sin (π) cosh (\frac{π}{2}) + i cos (π) sinh (\frac{π}{2})

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

Use the following trivial identity:

sin (π) = 0

Rewrite using trig identities:

cosh (\frac{π}{2}) = \frac{e ^{π} + 1}{2 e ^{\frac{π}{2}}}

Use the following trivial identity:

cos (π) = (- 1)

Rewrite using trig identities:

sinh (\frac{π}{2}) = \frac{e ^{π} - 1}{2 e ^{\frac{π}{2}}}

= 0 \cdot \frac{e ^{π} + 1}{2 e ^{\frac{π}{2}}} + i (- 1) \frac{e ^{π} - 1}{2 e ^{\frac{π}{2}}}

Simplify

0 \cdot \frac{e ^{π} + 1}{2 e ^{\frac{π}{2}}} + i (- 1) \frac{e ^{π} - 1}{2 e ^{\frac{π}{2}}} : i \frac{1 - e ^{π}}{2 e ^{\frac{π}{2}}}

= i \frac{1 - e ^{π}}{2 e ^{\frac{π}{2}}}

- 1.2 \cdot 1 8^{2} \cdot cos (18 \cdot 0.25 + \frac{π}{4})

2 cos (\frac{5 π}{4}) - (\frac{5 π}{4})

cos (25 2^{\circ})

\frac{27.3 sin ( 29. 8 ^{\circ} )}{5 cos ( 3 0 ^{\circ} )}

arctan (\frac{1}{100})

What is the value of sin(pi+i*pi/2) ?
The value of sin(pi+i*pi/2) is i(1-e^pi)/(2e^{pi/2)}