The height, h , in feet of a ball suspended from a spring as a function of time, t , in seconds can be modeled by the equation h is equal to negative 2 sine open paren pi times open paren t plus 1 half close paren close paren plus 5 Which of the following equations can also model this situation?
Answer
A
h is equal to negative 2 cosine pi t plus 5
B
h is equal to 2 cosine pi t plus 5
C
h is equal to negative 2 cosine open paren pi times open paren t plus 1 half close paren close paren plus 5
D
h is equal to 2 cosine open paren pi times open paren t plus 1 half close paren close paren plus 5
Explanation
Use the identity sin(x + π/2) = cos(x). Since π(t + 1/2) = πt + π/2, the original expression becomes h = -2 cos(πt) + 5. This matches choice B, which has the same amplitude, cosine function, and vertical shift.
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