The answer will be option C: y = 2cos3Θ the maximum of 2, the minimum value of -2 and period of 2π/3.
What is the range of cosine function?
The cosine function is the trigonometrical function that ranges between -1 and 1 at values of 0,π, and 2π for a period.
What is the period of a function?
The period of a function is defined only for a function that systematically repeats its range after a specific interval.
What is the period of a cosx function?
The cosx function ranges from 1 to -1 in the range of [0,2π], it is natural to think that the cosx function repeats itself after [0, π] which is not true as for a period the value it started should end with the same value. So cosx starts with a value of 1 at 0 and ends with a value of 1 at 2π.
Answer to the question:
So according to the question,
we have to find the cosine function having
1. the maximum of 2,
2. the minimum value of -2 and
3. period of 2π/3.
As we know cosine function ranges from -1 to 1 we can make it range from -2 to 2 by multiplying it by 2. So let the function be 2cosx.
also, we know that the period of the function should be 2π/3, so cosx should repeat after 2π/3 and we know the time period is 2π so if we multiply the angle by 3 we get the same time period. Hence x = 3Θ
So the final answer to the problem is y = 2cos3Θ.
Learn more about period of a function here
https://brainly.com/question/12634120
#SPJ2
