Question #0a9ed

1 Answer

theta = 102^@ (1.78"rad")

and

theta = 282^@ (4.92"rad")

The original condition repeats at any integer multiple of a full rotation of these angles.

Explanation:

According to reciprocal identities, tan(x) = 1/cot(x).
Therefore, cot(x)=-0.2122 is equal to tan(x)=1/-0.2122.

The tangent function is negative in the 2nd and 4th quadrant, and the inverse tangent function returns negative angles for negative values. To convert the negative angle into the two possible angles, we need to add 180^@ and 360^@, respectively:

theta = 180^@ + tan^-1(1/-0.2122)

and

theta = 360^@ + tan^-1(1/-0.2122)

theta = 180^@ - ~78^@

and

theta = 360^@ - ~78^@

theta = 102^@

and

theta = 282^@

The process is the same for radians but you add pi and 2pi respectively.

theta ~~ 1.78 and theta ~~ 4.92