Q. What is the period ofy=cos(−4πx+3)−7?Give an exact value.units
Finding the Period: The period of a cosine function, y=cos(Bx), is given by the formula period=∣B∣2π. In the given function y=cos(−4πx+3)−7, the coefficient B in front of x is −4π.
Using the Formula: To find the period, we use the formula with B=−4π. So, period =∣−4π∣2π.
Calculating Absolute Value: Calculate the absolute value of B, which is ∣−4π∣=4π.
Substituting into the Formula: Now, substitute 4π into the formula to get the period: period = 4π2π.
Simplifying the Fraction: Simplify the fraction by dividing 2π by 4π, which gives us period = 21.
Final Result: The period of the function y=cos(−4πx+3)−7 is 21 units.
More problems from Do the ratios form a proportion: word problems