what value of theta satisfies the equation sin(3theta+5)=cos(4theta+1)?

I was working on this same problem, but my answer needs to be in imperial minims.

Can you convert it to that? 

what value of theta satisfies the equation sin(3theta+5)=cos(4theta+1)?

I have assueed that theta is in radians.

You can see the graph that I have drawn.  Each root - where it crosses the x (theta) axis - is a soution to this equation,

so for any interval of 2pi there will be 8 different answers   

That is   for any interval   $$a\le \theta \le a+2\pi$$     there will be 8 solutions to this equation.

https://www.desmos.com/calculator/campy4wccp

If you would like me to discuss  this further I can.  

Another mathematician may also like to comment.

tx for the information but i wanted theta in degrees. do u know that?

No I did not know that.  How could I know that when you did not say that?

Anyway.

Here is the same equation in degrees

https://www.desmos.com/calculator/039twi8dlz

You can see the graph that I have drawn.  Each root - where it crosses the x (theta) axis - is a soution to this equation,

so for any interval of 360° there will be 8 different answers   

That is   for any interval   $$a\le \theta \le a+360$$     there will be 8 solutions to this equation.

I don't know I was going to try and convert to metric maxims.   

Imperial minims sound even worse!