For this question we will use the following formulas:
[tex]\begin{gathered} \sin \theta=\frac{y}{\sqrt[]{x^2+y^2}}, \\ \sec \theta=\frac{\sqrt[]{x^2+y^2}}{x}, \\ \tan \theta=\frac{y}{x}, \\ \text{where (x,y) is the point on a terminal side of }\theta. \end{gathered}[/tex]
Substituting the given data we get:
[tex]\begin{gathered} \sin \theta=\frac{3}{\sqrt[]{3^2+4^2}}=\frac{3}{\sqrt[]{9+16}}=\frac{3}{\sqrt[]{25}}=\frac{3}{5}, \\ \sec \theta=\frac{\sqrt[]{3^2+4^2}}{4}=\frac{\sqrt[]{9+16}}{4}=\frac{\sqrt[]{25}}{4}=\frac{5}{4}, \\ \tan \theta=\frac{3}{4}\text{.} \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} \sin \theta=\frac{3}{5}, \\ \sec \theta=\frac{5}{4}, \\ \tan \theta=\frac{3}{4}\text{.} \end{gathered}[/tex]
