Answer
1. $sin(\theta)= \frac{3}{5}$.
2. $cos(\theta)= \frac{4}{5}$.
3. $tan(\theta)= \frac{3}{4}$.
4. $cot(\theta)= \frac{4}{3}$.
5. $sec(\theta)= \frac{5}{4}$.
6. $csc(\theta)= \frac{5}{3}$.
Work Step by Step
Given point $(\frac{1}{3},\frac{1}{4})$, we have $x=\frac{1}{3}, y=\frac{1}{4}, r=\sqrt {(\frac{1}{3})^2+(\frac{1}{4})^2}=\frac{5}{12}$, we have:
1. $sin(\theta)= \frac{y}{r}= \frac{\frac{1}{4}}{\frac{5}{12}}=\frac{3}{5}$.
2. $cos(\theta)= \frac{x}{r}= \frac{\frac{1}{3}}{\frac{5}{12}}=\frac{4}{5}$.
3. $tan(\theta)= \frac{y}{x}=\frac{\frac{1}{4}}{\frac{1}{3}}=\frac{3}{4}$.
4. $cot(\theta)=\frac{1}{tan(\theta)}=\frac{4}{3}$.
5. $sec(\theta)=\frac{1}{cos(\theta)}=\frac{5}{4}$.
6. $csc(\theta)=\frac{1}{sin(\theta)}=\frac{5}{3}$.