Looking at the unit circle: tanӨ = tan(Ө <span>± 180k) If we add/subtract 180° from our angle, it simply ends up on the other side of the unit circle. Since tan</span>Ө is represented as slope, the values of the two are the same.
cotӨ is defined as the reciprocal of tanӨ (1/tanӨ) If tanӨ = tan(Ө ± 180k), then we could also say that 1/tanӨ = 1/tan(Ө ± 180k) which then becomes cotӨ = cot(Ө ± 180k)
Let's apply this to cot(290°). Subtract 180° to find that cot(290°) = cot(110°)
cot(110°) = -cot(70°) because the angle has been reflected across the y axis, making its slope opposite.
-cot(70°) = -1/tan(70°) because of that reciprocal property from earlier tan(70°) ≈ 2.75 -1/tan(70°) ≈ -0.36 = cot(290°)
(of course, most calculators can handle tan(110°), but if you're using a trig chart it might not be on there. include whichever steps are necessary)
