solving complex equation using euler's formula

Not sure where this belonged in the forum, but hopefully I got close.

I need to find values for c and x, that are both real and positive that satisfy this equation. Im pretty sure that Euler's formula will be of use, I cant figure out what the first step would be. Thanks.

cos(4t-1) - 2sin(4t+2) = c cos(4t+x)

Re: solving complex equation using euler's formula

Quote:

Originally Posted by

**snaes** Not sure where this belonged in the forum, but hopefully I got close.

I need to find values for c and x, that are both real and positive that satisfy this equation. Im pretty sure that Euler's formula will be of use, I cant figure out what the first step would be. Thanks.

cos(4t-1) - 2sin(4t+2) = c cos(4t+x)

This requires the application of trig identities to the left hand side to reduce it to the form of the left hand side.

What have you tried?

CB

Re: solving complex equation using euler's formula

I tried splitting these up with trig identities before and got:

cos(1)cos(4t) + sin(1)sin(4t) - 2cos(4t)sin(2) + 2cos(2)sin(4t)

Next, I factored out the constants. getting:

[cos(1)-2sin(2)]cos(4t) + [sin(1)+2cos(2)]sin(4t).

Now I just gotta find a way to combine these and just get a cosine term on the left side so that it will match the right.

Re: solving complex equation using euler's formula

Re: solving complex equation using euler's formula

Quote:

Originally Posted by

**snaes** I tried splitting these up with trig identities before and got:

cos(1)cos(4t) + sin(1)sin(4t) - 2cos(4t)sin(2) + 2cos(2)sin(4t)

Next, I factored out the constants. getting:

[cos(1)-2sin(2)]cos(4t) + [sin(1)+2cos(2)]sin(4t).

Now I just gotta find a way to combine these and just get a cosine term on the left side so that it will match the right.

Try putting

and:

CB

Re: solving complex equation using euler's formula

This worked great thanks! It just took me a while, because I messed up a negative sign for a while...

Quote:

Originally Posted by

**CaptainBlack** Try putting

and:

CB

Re: solving complex equation using euler's formula

Just to follow up - I got close with this but couldnt finish it this way. I did get the answer I was looking for with the other route. Thanks!

Quote:

Originally Posted by

**chisigma** Your original idea to use Euler's formula seems to me pretty good!... remember that from the Euler's formula...

(1)

... You can derive the identities...

(2)

(3)

What I suggest to You is to write all sin and cos in Your equation in 'exponential form' and then to set, for example,

...

Kind regards