How would I algebraically rearrange the equations [(sin(theta)+.5cos(theta))/(cos(theta)-.5sin(theta))]=3.4938 in order to find which value of theta satisfies

First you could multiply both sides of the equation by (cos(theta) - 0.5sin(theta)) to get:

 

sin(theta) + 0.5cos(theta) = 3.4938cos(theta) - 1.749sin(theta)

 

Then you could subtract 0.5 cos(theta) from both sides and add 1.749sin(theta) to get:

 

2.749sin(theta) = 2.9938cos(theta)

 

Now divide both sides by 2.749 to get:

 

sin(theta) = 1.089cos(theta) ----> (Keep in mind I rounded this number so be sure to include this number in your calculations in its full form).

 

Now divide both sides by cos(theta) to get:

 

sin(theta)/cos(theta) = 1.089

 

This simplifies to:

 

tan(theta) = 1.089 ----> (sin(x)/cos(x) is always equal to tan(x))

 

Now use the inverse tangent function to get:

 

47.44 degress or 0.8280 radians.