Find the upper and lower bound of trigonometric functions
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I've been tasked with finding the upper and lower bounds of the element:
A=sin(π.n2n+3)|n∈NA=sin(π.n2n+3)|n∈N
I think I have found the upper bound by doing:
limn→+∞sin(π.n2n+3)=limn→+∞sin(π.n2n)=limn→+∞sin(π2)=1limn→+∞sin(π.n2n+3)=limn→+∞sin(π.n2n)=limn→+∞sin(π2)=1
And since every point of sin(x)sin(x) is confined within [-1,1], the upper bound can only be 1
But I'm completely stumped as to how I can find the lower bound.
A=sin(π.n2n+3)|n∈NA=sin(π.n2n+3)|n∈N
I think I have found the upper bound by doing:
limn→+∞sin(π.n2n+3)=limn→+∞sin(π.n2n)=limn→+∞sin(π2)=1limn→+∞sin(π.n2n+3)=limn→+∞sin(π.n2n)=limn→+∞sin(π2)=1
And since every point of sin(x)sin(x) is confined within [-1,1], the upper bound can only be 1
But I'm completely stumped as to how I can find the lower bound.
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