Write the number of points of intersection of the curves $2 y = - 1 and y = cosec x$ .

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Solution

Given:
$2 y = - 1$ and $y = cosec x$
Now,
$2 y = - 1 \Rightarrow y = - \frac{1}{2}$
Also,

$cosec x = y \Rightarrow cosec x = - \frac{1}{2} \Rightarrow \frac{1}{\sin x} = - \frac{1}{2} \Rightarrow \sin x = - 2$

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.

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