a)
Because the min value of the function = -6: a+bcosx=−6
max value = 2: a+bcosx=2
Because −1≤cosx≤1 it means min(cosx)=−1,max(cosx)=1
Make up a system:{a+b(−1)=−6a+b∗1=2 ⟹ {a−b=−6a+b=2 ⟹ {2a=−4a+b=2 ⟹{a=−2b=4
Answer:f(x)=−2+4cosx
b)
−2+4cosx=0,x∈[0;2π]
4cosx=2⟹cosx=42⟹cosx=21
x=+− 3π+2πn,n∈Z,Z= set of integer
for n=0: x=3π and x=−3π - not suitable
for n=1:x=3π+2π - not suitable, and x=−3π+2π=35π
for n=−1:x=3π−2π - not suitable, and x=−3π−2π - not suitable
Answer: x=3π,x=35π
c)
The required plot of the graph between the blue and green line in the screenshot
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