Solving Trigonometric Equations

Question

 Find all solutions to the equation with . Give an exact answer if possible, otherwise give value(s) of  accurate to at least four decimal places.

4tan(a)+9=7

I found the arctan of -1/2, (2.6779) but it says there is still another answer, but I do not know how to find it.

Thank you in advance!

Answer 1

Solving the equation 4Tan(x)+9 = 7 gives Tan(x) = -(1/2)

Putting that in the calculator gives x = Tan-1 (-.5) = -26.565 degrees

Since the Tangent is negative in the 2nd and 4th quadrants, we add 180 degrees to -26.565 degrees to obtain

153.435 degrees.