solve for cot(x) = .3
since cot(x) = 1/tan(x), solve for 1/tan(x) = .3
multiply both sides by tan(x) and divide both sides by .5 to get:
tan(x) = 1/.3 = 73.30075577 degrees.
that's in the first quadrant which makes it the reference angle.
cotangent is negative in the second and fourth quadrants.
your angle will therefore be in the second and fourth quadrant.
the equivalent angle in the second quadrant is 180 minus 73.30075577 = 106.6992442 degrees.
the equivalent angle in the fourth quadrant is 360 minus 73.30075577 = 286.6992442 degrees.
use your calculator to find 1/tan(each of those angles) = -.3
this is cot(x) = -.3 looks like on a graph.
note that this is only in the 0 to 360 degree range.
since the cot(x) funcion repeats every 180 degrees, then the full answer would be:
cot(x) = 106.6992442 degrees plus or minus 180 * k where k is a positive integer greater than or equal to 0.
alternatively, you could say:
cot(x) = 286.6992442 degrees plus or minus 180 * k where k is a posiive integer greater than or equal to 0.
for example, when the angle is 106.699 degrees, then:
k = 0 gets you 106.699
k = 1 gets you 286.699
k = 2 gets you 466.699
k = 3 gets you 646.699
k = -1 gets you -73.305
k = -2 gets you -253.301
this can be seen on the graph.
the primary domain of x would be 0 to 180 degrees.
that gets you 106.699 = 106.7 degrees as the most likely answer.
since the domain of x was not specified, however, then the answer as shown below would be applicable.
cot(x) = 106.7 degrees plus or minus 180 * k where k is a positive integer greater than or equal to 0.