The function f is defined, for x \geq 0 ,

Porter Mccullough

Porter Mccullough

Answered question

2022-04-19

The function f is defined, for x0 , by f(x)=43cos(x2)
Given that f(na+b)=2.5 where a is positive constant and n=0,1,2,..., find the smallest possible value of b and least value of a.

Answer & Explanation

belamontern9i

belamontern9i

Beginner2022-04-20Added 19 answers

Basically, we need to solve in (a,b) as:
43cos(na+b2)=2.5
cos(na+b2)=12=cosπ3
Note the solution to cosx=cosy is given by x=y+2πα, αZ
Thus, we get:
na+b2=π3+2πα
na+b=2π3+4πα

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