Don't really understand this math problem.

[InlineFour]

What is the period of y = Acos(x-Bp)?(Here x is in radians.)

 

[Heisenberg]

The period is the length between points where the function has identical values. For example, the period of regular sine and cosine is 2*Pi.

 

[DrPizza]

I know that Heisenberg knows what he means, but "between the points where the function has identical values" is correct, but incorrect if you're not considering enough values. i.e. Sin(Pi/4) and Sin(3Pi/4) both have the same value... but f'(x) doesn't have the same value.

For asin(bx+c) and acos(bx+c), the frequency is the number of "sin curves" you'll have between 0 and 2Pi. And, conveniently, is simply the value of b. The period is 2Pi / b.

Hopefully that helps also.

 

[Heisenberg]

Sorry, yeah the more correct definition is the shortest interval of the which the function repeats itself. I.e. if f(x+d) = f(x) then d is the period. Although what I said made perfect sense to me in my own head. 😛

 

[Hyperion042]

Not true - it's just 2Pi in this case. The period of a function f(x) is unchanged by simple additive elements on x - eg, the period of f(x) = the period of f(x+9) = the period of f(x+ab). All that matters here is your independent variable x.

In general, if you can transform one curve into another by simple translations and amplitude changes, they have the same period - in this case, the curve is just pushed a little to the right or left, so you just have to translate it back to where it was. Period is the same as cos(x) = 2Pi.

 

[DrPizza]

Originally posted by: Hyperion042
Not true - it's just 2Pi in this case. The period of a function f(x) is unchanged by simple additive elements on x - eg, the period of f(x) = the period of f(x+9) = the period of f(x+ab). All that matters here is your independent variable x.

In general, if you can transform one curve into another by simple translations and amplitude changes, they have the same period - in this case, the curve is just pushed a little to the right or left, so you just have to translate it back to where it was. Period is the same as cos(x) = 2Pi.

What's "not true"?

Neither Heisenberg, nor myself ever gave an answer; we just tried to give enough help that the OP would be able to answer the question himself. Heisenberg described what the period is first. Then, as I've had some students in my classes who do what I listed as a counter example of why Heisenberg's description wasn't quite right, I modified it slightly. Then, provided the means to find the frequency (in the OP's case, b, hopefully obviously, =1) and the period = 2Pi/b.

 

[LordMorpheus]

Originally posted by: Heisenberg
The period is the length between points where the function has identical values. For example, the period of regular sine and cosine is 2*Pi.

not quite true - a cosine will hit all the values in its range with the exceptions of the max and min twice in a period.

The period of a function is the length it takes to repeat itself - not all funtions are periodic, but cosines are. The function in question has a period of 2/B.