Question

Cos theta if tan theta equals 2/5

Answer 1

$\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan(\theta)=\cfrac{2}{5}\cfrac{\impliedby opposite}{\impliedby adjacent}\\\\ -----------------------------\\\\ \textit{using the pythagorean theorem then}\\\\ c^2=a^2+b^2\implies c=\pm \sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite \end{cases} \\\\\\ \textit{recall that }cos(\theta)=\cfrac{adjacent}{hypotenuse}$

so.. .to get the cosine from that, all we need is the "hypotenuse" or radius in that angle

now.... keep in mind that, there are two likely quadrants where the opposite and adjacent sides, or x and y, are both positive, or both negative

I and II quadrants, so on those two quadrants, the tangent will be positive, since both numerator an denominator have the same sign

but I gather in this case, it may be assumed is the first quadrant, namely, that is 2/5 as opposed to -2/-5, so the adjacent side is positive