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What is the period of the function 
h(x)=-3cos(pi x+2)-6?
Give an exact value.
units

What is the period of the function h(x)=3cos(πx+2)6? h(x)=-3 \cos (\pi x+2)-6 ? \newlineGive an exact value.\newlineunits

Full solution

Q. What is the period of the function h(x)=3cos(πx+2)6? h(x)=-3 \cos (\pi x+2)-6 ? \newlineGive an exact value.\newlineunits
  1. Period of cosine function: The period of a cosine function of the form h(x)=Acos(Bx+C)+D h(x) = A \cos(Bx + C) + D is given by 2πB \frac{2\pi}{|B|} . In our function h(x)=3cos(πx+2)6 h(x) = -3 \cos(\pi x + 2) - 6 , the coefficient B in front of x is π \pi .
  2. Calculating the period: Calculate the period using the formula 2πB \frac{2\pi}{|B|} with B=π B = \pi .\newlinePeriod = 2ππ \frac{2\pi}{|\pi|} = 2ππ \frac{2\pi}{\pi} = 22.
  3. No math error in calculation: Since the period is a positive value and we have calculated it using the correct formula, there is no math error in the calculation.

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