Question

What is the period for the function y = -4 cos (5x +3)? (4.3)

Answer 1

The periodicity of function is $\frac{2 \pi}{5}$

Solution:

Given that we have to find the period of function

Given function is:

$y = -4 + cos(5x+3)$

Use the below formula:

$\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}$

Thus,

$Peridocity\ of\ cos(5x + 3) - 4 = \frac{\text{periodicity of cos(x)}}{5}$

Now find the periodicity of cos(x)

We know that,

periodicity of cos(x) = $2 \pi$

Therefore,

$Peridocity\ of\ cos(5x + 3) - 4 = \frac{2 \pi}{5}$

Thus the periodicity of function is $\frac{2 \pi}{5}$