Question

I need help with this work for my pre calculus class

Answer 1

Answer:

$\begin{gathered} \frac{\sin \theta}{\cos \theta} \\ \\ \frac{1}{\cot \theta} \end{gathered}$

Explanation:

Let's consider the below right triangle;

From the above, we can see that sin0/cos0 is equivalent to tan0;

$\begin{gathered} \sin \theta=\frac{a}{b} \\ \cos \theta=\frac{c}{b} \\ \tan \theta=\frac{a}{c} \\ \frac{\sin \theta}{\cos \theta}=\frac{\frac{a}{b}}{\frac{c}{b}}=\frac{a}{b}\times\frac{b}{c}=\frac{a}{c} \end{gathered}$

We also know that;

$\begin{gathered} cot\theta=\frac{1}{\tan \theta} \\ \tan \theta=\frac{1}{\cot \theta} \end{gathered}$