Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the period of

y=cos(-4pi x+3)-7?
Give an exact value.
units

What is the period of\newliney=cos(4πx+3)7? y=\cos (-4 \pi x+3)-7 ? \newlineGive an exact value.\newlineunits

Full solution

Q. What is the period of\newliney=cos(4πx+3)7? y=\cos (-4 \pi x+3)-7 ? \newlineGive an exact value.\newlineunits
  1. Finding the Period: The period of a cosine function, y=cos(Bx)y = \cos(Bx), is given by the formula period=2πB\text{period} = \frac{2\pi}{|B|}. In the given function y=cos(4πx+3)7y = \cos(-4\pi x + 3) - 7, the coefficient BB in front of xx is 4π-4\pi.
  2. Using the Formula: To find the period, we use the formula with B=4πB = -4\pi. So, period =2π4π= \frac{2\pi}{|-4\pi|}.
  3. Calculating Absolute Value: Calculate the absolute value of B, which is 4π=4π|-4\pi| = 4\pi.
  4. Substituting into the Formula: Now, substitute 4π4\pi into the formula to get the period: period = 2π4π\frac{2\pi}{4\pi}.
  5. Simplifying the Fraction: Simplify the fraction by dividing 2π2\pi by 4π4\pi, which gives us period = 12\frac{1}{2}.
  6. Final Result: The period of the function y=cos(4πx+3)7y = \cos(-4\pi x + 3) - 7 is 12\frac{1}{2} units.

More problems from Do the ratios form a proportion: word problems