Question

If 0 is an angle in quadrant II, what is the value of cos0?

Answer 1

in the II Quadrant, let's recall that the adjacent side or cosine is negative whilst the opposite side or sine is positive, thus

`tan(\theta )=-\sqrt{\cfrac{19}{17}}\implies tan(\theta )=\cfrac{\stackrel{opposite}{√(19)}}{\underset{adjacent}{-√(17)}}\impliedby \qquad \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2+b^2) \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}`

`c=\sqrt{(-√(17))^2~~ + ~~(√(19))^2}\implies c=√(17+19)\implies c=√(36)\implies c=6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-√(17)}}{\underset{hypotenuse}{6}}~\hfill`