Question

the point (x, y) is on the terminal side of angle $\vartheta$in standard position. Find the exact value of the given trigonometric function

$(2,7),\sin \vartheta$

Short answer

$\sin \vartheta =\frac{7}{\sqrt{53}}$

Step-by-step solution

Step 1. Given information

$(2,7),\sin \vartheta$

Step 2. Solving for sinϑ

We know that for any given point (x,y)

$$\begin{gathered} \sin \vartheta =\frac{y}{r} \\ r=\sqrt{x^2+y^2} \end{gathered}$$

Using this :

$$\begin{gathered} \sin \vartheta =\frac{y}{r} \\ \sin \vartheta =\frac{7}{\sqrt{2^2+7^2}} \\ \sin \vartheta =\frac{7}{\sqrt{53}} \end{gathered}$$