Q. 22 - Precalculus Enhanced with Graphing Utilities

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

 $(2,7), \sin \vartheta$

Step-by-Step Solution

Answer

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

Step 1. Given information

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

Step 2. Solving for sin ϑ

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 :

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