Question

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Problem 31? Can someone please explain how to begin with this?

Answer 1

So you're looking for the amplitude and period of y=1/2cos(x+pi/6) right?

Answer 2

Yes.

Answer 3

So the period is how long it takes to do one complete oscillation before it repeats all over again. So in order to find out when that is, what is the smallest value of x can you plug in so that y(x)=y(x+a).

So for instance, sine and cosine repeat after 2pi. sin(x)=sin(x+2pi). Play around with it on a graphing calculator and you'll see what I mean, it's worth the time to sort of play with them to see how it will change how they behave.

Now what about amplitude? Well sine and cosine are defined as being on the unit circle, so they have an amplitude of 1. Whatever number you multiply them by is what the amplitude becomes, since you're essentially multiplying by 1, which can be thought of as the radius of a circle.

Answer 4

@Kainui
Can this be done with out a calculator?

Answer 5

Yes, but at this point you don't have any experience with sine and cosine functions, so you don't know what all the parts are. It's much better if you play around and see the difference between what these functions look like:

2sinx and 5sinx
sin(x) and sin(4x)
sin(x+pi), cos(x) and sin(x+pi/2)

and just sort of change one thing at a time. As long as you know what the amplitude is (How high it wobbles from the x-axis) and the period (how long it takes to repeat itself) you should be able to figure out what part of the function changes what.

Also, you could draw it on paper. =)

Answer 6

Sinusiodal Equation : y=A cos (wx+theta)
Amplitude = A
Phase = theta
Period T = 2pi/w