Question

What is the period of y = 8 cos (5pie x + 3pie/2)-9 Give an exact value. Units

Answer 1

Answer:

$\textsf{Period}=\dfrac{2}{5}$

Step-by-step explanation:

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

• A = amplitude (height from the mid-line to the peak)
• 2π/B = period (horizontal distance between consecutive peaks)
• C = phase shift (horizontal shift - positive is to the left)
• D = vertical shift

Given function:

      $y= 8 \cos \left(5 \pi x+\dfrac{3 \pi}{2}\right)-9$

$\implies y= 8 \cos \left(5 \pi \left(x+\dfrac{3}{10}\right)\right)-9$

Comparing with the standard form:

$\implies \textsf{B}=5 \pi$

$\implies \textsf{Period}=\dfrac{2 \pi}{\sf B}=\dfrac{2 \pi}{5 \pi}=\dfrac{2}{5}$

Answer 2

$\\ \rm\Rrightarrow y=Acos(Bx+C)+D$

• This is the general formula and the period is 2π/B

Now our given function

$\\ \rm\Rrightarrow y=8cos\left(5\pi x+\dfrac{3\pi}{2}\right)-9$

On comparing we get

• A=8
• B=5π
• C=3π/2
• D=-9

Period:-

$\\ \rm\Rrightarrow \dfrac{2\pi}{B}$

$\\ \rm\Rrightarrow \dfrac{2\pi}{5\pi}$

$\\ \rm\Rrightarrow \dfrac{2}{5}$