Question

How am I supposed to figure this out if csc Theta(0) has a radical number on the top?

Answer 1

$\bf csc(\theta)=\cfrac{hypotenuse}{opposite}\implies csc(\theta)=\cfrac{\sqrt{7}}{2}\cfrac{\leftarrow hypotenuse=c}{\leftarrow opposite=b}\\\\ -----------------------------\\\\ \textit{so hmm using the pythagorean theorem, we can say that}\\\\ c^2=a^2+b^2\implies \pm \sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ b=opposite\\ a=adjacent \end{cases}\\\\ \textit{we'll assume is the + of the root, since you're not}\\ \textit{given further info on it, that means the I quadrant}$

$\bf -----------------------------\\\\ cos(\theta)=\cfrac{a}{c}\qquad sec(\theta)=\cfrac{c}{a}\qquad tan(\theta)=\cfrac{b}{a}\qquad cot(\theta)\cfrac{a}{b}$

so just find the "adjacent" side, using the pythagorean theorem, and even though the square root can give you +/-, use the positive one, assuming the angle is in the 1st quadrant

keeping in mind, that the 2nd quadrant is feasible as well, since the opposite side of +2 can also be in the 2nd quadrant

but anyhow, use the I quadrant