simplify the equation by putting it into tan(ax+b)=c and use the inverse tan to solve for x

Question

find the decimal answer and the exact answer

1=30tan(5x+8)-4

Answer 1

First we want to get the equation into the form tan(ax+b) = c

(30)tan(5x+8) - 4 = 1

(30)tan(5x+8) = 5

tan(5x+8) = 5/30 = 1/6

Then we use arctan to solve for x

tan^-1(tan(5x+8)) = tan^-1(1/6)

5x+8 = tan^-1(1/6)

5x = tan^-1(1/6) - 8

x = (tan^-1(1/6) - 8)/5

Plugging that into the calculator we get x = 0.29246

Answer 2

I am assuming they want the answer in degrees. If they want the answer in radians, do the same steps but change your calculator to radian mode when you do the calculations.

1 = 30tan(5x + 8) - 4

5 = 30tan(5x + 8)

1/6 = tan(5x + 8)

tan^-1(1/6) = 5x + 8

tan^-1(1/6) - 8 = 5x

(tan^-1(1/6) - 8)/5 = x

0.292 = x