Question

period 5 sin5x cos 3x

Answer 1

Answer:

Period is $\pi$

Step-by-step explanation:

To find the period of $y = 5 \sin(5x) \cos(3x)$

Suppose two positive integers $m$ and $n$

The period of

$\sin(5x) = \frac{2\pi}{5} = p$

and of

$\cos(3x) = \frac{2\pi}{3} = q$

Suppose,

$np = mq = r$

$\frac{n}{m} = \frac{5}{3}$

$np = 2k\pi$

, where $k = \frac{1}{2}$

hence period is $r = \pi =$period

Please mark brainliest...

There is another way

$5 \sin(5x) \cos(3x) = 5 \frac{\sin(8x) +\cos(2x)}{2}$

Thus the period will be lcm of $\frac{2\pi}{8}$ and $\frac{2\pi}{2}$

which is found to be $\pi$...

Answer 2

Answer:

Period is π

Hope it helps