Question

Evaluate cot 290º. Round your answer to the nearest hundredth. Explain each step

Answer 1

Looking at the unit circle:
tanӨ = tan(Ө ± 180k)
If we add/subtract 180° from our angle, it simply ends up on the other side of the unit circle. Since tanӨ 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)