The number of solutions of | x| = x, such that -4 x 4 is:

Question

The number of solutions of $|\cos x| = \sin x$, such that $-4\pi \le x \le 4\pi$ is:

Accepted Answer

Period of $$|\cos x| = \pi $$

And period of $$\sin x = 2\pi $$

Graph of $$\sin x$$ and $$|\cos x|$$ cuts each other at two points A and B in $$\left[ {0,2\pi } \right]$$

So, in $$\left[ { - 4\pi ,4\pi } \right]$$, total 4 similar graph will be present and graph of $$\sin x$$ and $$|\cos x|$$ will cut $$4 \times 2 = 8$$ times.

$$\therefore$$ Total possible solutions = 8.

Solutions · 1