Question

.Provide two inequalities that establish e^cos(n)  = Big Theta(1). Indicate the constant being used for each inequality. Justify your answer.

Answer 1

.Provide two inequalities that establish e^cos(n)  = Big Theta(1). Indicate the constant being used for each inequality. Justify your answer.

The minimum value of cos(n) = 0 for n = 90 degrees.

The maximum value of cos(n) = 1 for n = 0.

This means that the range of cos(n) is:

0 <= cos(n) <= 1

Hence, the values of e^cos(n) varies from

e⁰ <= e^cos(n) <= e¹

=> 1 <= e^cos(n) <= 2.71828

This proves that e^cos(n)  = Big Theta(1).