Question

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]

Answer 1

Given: 

2y = -1 and y= cosec x

Now,
2y = -1`=>`y = -`1/2`

\[cosecx = y\]

\[ \Rightarrow cosecx = - \frac{1}{2}\]

\[ \Rightarrow \frac{1}{\sin x} = - \frac{1}{2}\]

\[ \Rightarrow \sin x = - 2\]
The value of sine function lies between - 1 and 1. Therefore, the two curves will not intersect at any point.

Hence, the number of points of intersection of the curves is 0.