Find expert answers and community insights on IDNLearn.com. Discover in-depth and trustworthy answers to all your questions from our experienced community members.
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

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.