SOLUTION: Consider the trigonometric function f(t)= 6 + 4cos(4πt). (i) What is the amplitude of f(t)? (ii) What is the period of f(t)? (iii) What are the maximum and minimum val

Algebra ->  Trigonometry-basics -> SOLUTION: Consider the trigonometric function f(t)= 6 + 4cos(4πt). (i) What is the amplitude of f(t)? (ii) What is the period of f(t)? (iii) What are the maximum and minimum val      Log On


   

Question 511712: Consider the trigonometric function f(t)= 6 + 4cos(4πt).
(i) What is the amplitude of f(t)?
(ii) What is the period of f(t)?
(iii) What are the maximum and minimum values attained by f(t)?
(iv) Sketch the graph of f(t) for t ∈ [0,1].
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the trigonometric function f(t)= 6 + 4cos(4πt).
Form: y = a*cos(bx-c) + d
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a = 4 ; b = 4(pi) ; c = 0 ; d = 6
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(i) What is the amplitude of f(t)?::: |a| = 4
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(ii) What is the period of f(t)?::: P = (2pi)/b = (2pi)/(4pi) = (1/2)
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(iii) What are the maximum and minimum values attained by f(t)?
Because the cos graph is moved up 6, max = 4+6 = 10, min = -4+6 = 2
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(iv) Sketch the graph of f(t) for t ∈ [0,1].
graph%28400%2C400%2C-10%2C10%2C-5%2C15%2C4cos%283.14x%29%2B6%29
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Cheers,
Stan H.
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