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A weight hangs on the end of an elastic string. The weight is pulled down and released from rest at time t = 0. The length x centimeters of the string at time t seconds is given by the formula: x = 7 - 2sin(πt)

a) Sketch the graph of x against t for 0 <= x <=4

b) Find the two times at which the length of the string is least and the values of x at those times

c) After how many seconds does the weight return to its starting point for the first time?

**My Answers**

b) So, I started out by thinking about what would be the least length for the function sin(x). I got to the conclusion it was -1, which is equal to an angle of -π/2 radians or 1.5π radians. Applying the angle in the formula gave me 9 while the correct answer is 5. The answer 5 is obtained when using sin(1) instead of sin(-1). Why?

Furthermore, the question asks for the times at which the value of x is the least

*the value of x itself. Is it possible to solve it in that order, because, what I did next was:*

__before__5 = 7 - 2sin(πt)

and solved for t, finding 0.5. But I don't know how to find the second answer and I don't even know where to start for letter C...

Any help appreciated.