Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

use the circle unit to evaluate csc(-/2)

Sagot :

The definition of the cosecant function is

[tex]\csc \theta=\frac{1}{\sin \theta}[/tex]

Therefore,

[tex]\Rightarrow\csc (-\frac{\pi}{2})=\frac{1}{\sin (-\frac{\pi}{2})}[/tex]

To find sin(-pi/2), use the diagram below.

Consider that the circumference has a radius equal to 1. Then, the coordinates of the orange point are (0,-1). Furthermore, the points on the circumference are given as (cos(theta), sin(theta)); therefore,

[tex]\begin{gathered} \Rightarrow(0,-1)=(\cos (-\frac{\pi}{2}),\sin (-\frac{\pi}{2})) \\ \Rightarrow\sin (-\frac{\pi}{2})=-1 \\ \Rightarrow\csc (-\frac{\pi}{2})=\frac{1}{-1}=-1 \\ \Rightarrow\csc (-\frac{\pi}{2})=-1 \end{gathered}[/tex]

Thus, the answer is csc(-pi/2)=-1

View image ElzaW758882
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.