1c. graph ( y=cos (x) ) over the interval ( -2 pi leq x leq 2 pi ).\n1d. how many cycles of the cosine curve…

Explanation:

Step1: Recall the period of the cosine function

The period of ( y = \cos(x) ) is ( 2\pi ). This means that the function repeats its values every ( 2\pi ) units along the ( x )-axis.

Step2: Calculate the length of the given interval

The interval is from ( x=-2\pi ) to ( x = 2\pi ). The length of the interval ( L=2\pi-(-2\pi)=4\pi ).

Step3: Determine the number of cycles

To find the number of cycles ( n ), we use the formula ( n=\frac{\text{Length of interval}}{\text{Period of the function}} ). Substituting the values, we have ( n=\frac{4\pi}{2\pi} ).

Answer:

( 2 )