How Do You Solve the Equation 1=10*exp((-pi*t)/5)*cos(pi*t)?

[swain1]

Hi, can anyone help me to solve this equation for t please.

1=10*exp((-pi*t)/5)*cos(pi*t)

Thanks

 

[Tide]

HINT: Rewrite the equation as

$$10 \cos \left[ \pi t \left(1 - \frac {i}{5}\right) \right] = 1$$

Second HINT: Recheck my algebra! ;)

 

[mathman]

Note to Tide: Your algebra looks wrong.

 

[Tide]

mathman,

Yes, very! Thanks - but I did give fair warning. :)

[note to self: do it on paper next time!]

 

[HallsofIvy]

Hi, can anyone help me to solve this equation for t please.
1=10*exp((-pi*t)/5)*cos(pi*t)
Thanks

Either write cos(pi*t) as
$$\frac{e^{i\pit}+ e^{-i\pit}}{2}$$
so that the equation becomes
$$1= 10e^{-\frac{\pit}{5}}\(\frac{e^{i\pit}+ e^{-i\pit}}{2}\)= 5\(e^{\pit\(-\frac{1}{5}+ i\)+ e^{\pit\(-\frac{1}{5}- i\)\)$$
or write exp((-pi*t)/5) as
$$cos(-\frac{\pit}{5})+ i sin(-\frac{\pit}{5})$$
so the equation becomes
$$1= 10\(cos(\frac{\pit}{5}cos(\pit)- icos(\pit)sin(\frac{pit}{5})\)$$