Question

Let (4,3) be a point on a terminal side of Фfind the exact values of sinФ, secФ and tanФSinФ=secФ=TanФ=

Answer 1

For this question we will use the following formulas:

`\begin{gathered} \sin \theta=\frac{y}{\sqrt[]{x^2+y^2}}, \\ \sec \theta=\frac{\sqrt[]{x^2+y^2}}{x}, \\ \tan \theta=(y)/(x), \\ \text{where (x,y) is the point on a terminal side of }\theta. \end{gathered}`

Substituting the given data we get:

`\begin{gathered} \sin \theta=\frac{3}{\sqrt[]{3^2+4^2}}=\frac{3}{\sqrt[]{9+16}}=\frac{3}{\sqrt[]{25}}=(3)/(5), \\ \sec \theta=\frac{\sqrt[]{3^2+4^2}}{4}=\frac{\sqrt[]{9+16}}{4}=\frac{\sqrt[]{25}}{4}=(5)/(4), \\ \tan \theta=(3)/(4)\text{.} \end{gathered}`

Answer:

`\begin{gathered} \sin \theta=(3)/(5), \\ \sec \theta=(5)/(4), \\ \tan \theta=(3)/(4)\text{.} \end{gathered}`