Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

find an equation of a cosine function with maximum of 7, minimum of -7 and period of 7?

find an equation of a cosine function with maximum of 7, minimum of -7 and period of 7

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  • 1 month ago

    Let y = acos(bx)

    The period is 2π/b

    Hence, we require that 2π/b = 7

    so, b = 2π/7   

    Hence, y = acos(2πx/7)

    Finally, -1 ≤ cos(2πx/7) ≤ 1....i.e. minimum of -1 and maximum of 1

    Hence, -7 ≤ 7cos(2πx/7) ≤ 7 

    so, y = 7cos(2πx/7)

    A sketch is below.

    :)>

    Attachment image
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  • 1 month ago

    A = [max(val) - min(val)]/2

     A =[7 - (- 7)]/2

    A = 7

    midline = [max(val) + min(val)]/2

    midline = (7 - 7)/2 

    midline = 0

    P = 7

    P = 2π/k

    7 = 2π/k

    7k = 2π

     k = 2π/7

    y = 7cos(2π/7x) Answer//

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