Question
Given that $\sin \alpha=\frac{\sqrt{5}}{3}, \cos \alpha=\frac{2}{3},$ and$\tan \alpha=\frac{\sqrt{5}}{2},$ find $\csc \alpha, \sec \alpha,$ and $\cot \alpha$
Step 1
So, we have \[\csc \alpha = \frac{1}{\sin \alpha}.\] Substituting the given value of $\sin \alpha = \frac{\sqrt{5}}{3}$, we get \[\csc \alpha = \frac{1}{\frac{\sqrt{5}}{3}} = \frac{3}{\sqrt{5}}.\] To rationalize the denominator, we multiply the numerator and the Show more…
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