Calculate minimum and maximum and zeros fo function 3sinx.

Thanx, by.

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- November 28th 2009, 12:01 AMkapitalMinimum and maximum
Calculate minimum and maximum and zeros fo function 3sinx.

Thanx, by. - November 28th 2009, 12:15 AMStroodle
As the amplitude is 3 and there is no vertical translation or dilation parallel to the x-axis, the maximums would be at and the minimums would be at (where is an integer).

As for the zeros, there would also be infinitely many, since there is no domain specified.

If the domain were (i.e. one cycle of this particular function) the zeros would be at and

There's a good guide to basic trig graphs and functions here: http://www.purplemath.com/modules/triggrph.htm - November 28th 2009, 01:28 AMpurebladeknight
since there is no specified domain, i will make this general:

zeros occur when sin3x=0,

so y=sin3x crosses 0 when x=....-60,0,60, 120.... => x=kpi/3 where k is an integer

to find max/mins we differentiate y=sin3x

you get y'=3cos3x

when y'=0 you get stationary => max/min

3cos3x=0, when x=....,-90, -30,30, 90... => (2k-1)pi/6

the mins and maxes alternate (max when k is odd, and min when k is even)

edit: sorry misread Q, thought it was sin3x, but it is actually 3sinx, but i will still leave this incase anyone needs it