Write the number of points of intersection of the curves
Question:

Write the number of points of intersection of the curves $2 y=1$ and $y=\cos x, 0 \leq x \leq 2 \pi$.

Solution:

Given curves: $2 y=1$ and $y=\cos x$

Now,

$2 y=1 \Rightarrow y=\frac{1}{2}$

Also,

$\cos x=y$

$\Rightarrow \cos x=\frac{1}{2}$

$\Rightarrow \cos x=\cos \left(\frac{\pi}{3}\right)$ and $\cos x=\cos \left(\frac{4 \pi}{3}\right)$

$\Rightarrow x=2 n \pi \pm \frac{\pi}{3} \quad$ or $\quad x=2 n \pi \pm \frac{4 \pi}{3}$

By putting $n=0$, we get:

$x=\frac{\pi}{3}$ and $x=\frac{2 \pi}{3}$

For the other value of n,  the value of will not satisfy the given condition.

Hence, the number of points of intersection of the curves is two, i.e., $\frac{\pi}{3}$ and $\frac{4 \pi}{3}$.

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