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 \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}}}

arcsin (\frac{sin ( 4 5 ^{\circ} )}{1.41})

5 sin (5 3^{\circ})

arccos (\frac{1}{14})

arctan (\frac{2.55}{9.8} + 0.5)

sec (1 8^{\circ}) tan (1 8^{\circ}) cos (1 8^{\circ}) cot (1 8^{\circ})

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)}