Posted by **Becky** on Monday, March 5, 2007 at 5:14pm.

What is sin(i) -- (sin of the imaginary number, i)

What is cos(i)-- cosine of the imaginary number, i

orrr

tan(1+i)

You can derive these things from the equation:

Exp(i x) = cos(x) + i sin(x) --->

sin(x) = [Exp(ix) - Exp(-ix)]/(2i)

cos(x) = [Exp(ix) + Exp(-ix)]/2

tan(x) =

1/i * [Exp(ix) - Exp(-ix)]/[Exp(ix) + Exp(-ix)]

These relations are also valid for complex values for x. E.g.:

tan(1+i) =

1/i * [Exp(i-1) - Exp(-i+1)]/[Exp(i-1) + Exp(-i+1)]

Exp[i-1] = Exp[i]Exp[-1] = Exp[-1](cos(1)+isin(1))

Exp[-i+1] = Exp[-i]Exp[1] = Exp[1](cos(1)-isin(1))

## Answer This Question

## Related Questions

- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- algebra - Can someone please help me do this problem? That would be great! ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- precalculus - For each of the following determine whether or not it is an ...
- Trigonometry - Please review and tell me if i did something wrong. Find the ...
- Trigonometry - Solve the equation for solutions in the interval 0<=theta<...
- Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...

More Related Questions