Solve the equation for exact solution over the interval [0,2pie)

Question

3 cot x+ 4=7

Answer 1

x = pi/4 and 5pi/4

or x = 45 degrees and 225 degrees

3cot(x) + 4 = 7

3cotx = 7-4 = 3

cotx = 3/3 = 1

cotx =1

x = cot^-1(1) = pi/4, 5pi/4

(that's assuming you meant (3cotx) +4 = 7 and not 3cot(x+4) = 7, a fair likely assumption. Otherwise, 4 would likely mean 4 radians, since you specified the interval with 2pi. But if you meant cot(x+4), then cot(x+4) = 7/3, tan(x+4)=3/7 and x+4 = about 23.19859051 or 23.2 degrees = 0.12888 pi radians = .40489 radians

But if 4 meant 4 degrees, then x+4 = 23.1986 and x = 19.1986)