Question

Find the basic period and basic frequency of the function g(t)=8cos(10πt)+sin(15πt)

Answer 1

Answer:

The period is

$\frac{2\pi}{5}$

The frequency is

$\frac{5}{2\pi}$

Explanation:

The period of both functions will be LCM of both period.

The period of cos is

$\frac{\pi}{5}$

The period of sin is

$\frac{2\pi}{15}$

Let convert each into degrees.

$\frac{\pi}{5} = 36$

$\frac{2\pi}{15} = 24$

Find the least common multiple between 36 and 24, which is 72.

Convert 72 into radians

$72 = \frac{2\pi}{5}$

The period is 2pi/5.

The frequency is equal to

1/period.

so the frequency is

$\frac{1}{ \frac{2\pi}{5} } = \frac{5}{2\pi}$