Question

Find theta between 0 and 2pi of the point (2,-4). Round to the nearest hundredth.

Answer 1

check the picture below.

$\bf (\stackrel{x}{2}~,~\stackrel{y}{-4})\qquad tan(\theta )=\cfrac{y}{x}\implies tan(\theta )=\cfrac{-4}{2}\implies tan(\theta )=-2\\\\\\\measuredangle \theta =tan^{-1}(-2)\implies \measuredangle \theta \approx -63.44^o\implies \measuredangle \theta \approx \stackrel{360^o-63.44^o}{296.56^o}$

as you may already know, tan⁻¹ function has a range of (π/2, -π/2), and therefore it will give us the negative counterpart angle, however, the positive one we can get it by going the other way, 360 - θ.