Question

Let (-4,-5) be the point on the terminal side of theta find cos (theta), sec (theta) & cot (theta)

Answer 1

Check the picture below.

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2 + b^2) \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-4}\\ b=\stackrel{opposite}{-5}\\ \end{cases} \\\\\\ c=√((-4)^2 + (-5)^2)\implies c=√(41) \\\\[-0.35em] ~\dotfill`

`cos(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{√(41)}}\implies \cfrac{-4}{√(41)}\cdot \cfrac{√(41)}{√(41)}\implies -\cfrac{4√(41)}{41} \\\\\\ sec(\theta )\cfrac{\stackrel{hypotenuse}{√(41)}}{\underset{adjacent}{-4}}\implies -\cfrac{√(41)}{4}~\hfill cot(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{opposite}{-5}}\implies \cfrac{4}{5}`