BQ #2: Unit T Concept Intro

a) Why are the periods for sin and cos 2pi and the period for tan only pi?

If we look at all the signs that we have when looking at a sin graph, we can see that the order of this is; +,+,-,- this pattern does not repeat, therefore we need to have another cycle and then it will repeat, each of these cycles is equal to pi, therefore this graph's period will be 2pi

As for the cosine graph, the cycle is +,-,-,+ so we can see once again that the signs don't repeat themselves yet, therefore we had to once again add another cycle and make this period be 2pi.

When we look at the tan/cot graph however, we see that the cycle is +,-,+,- in this case the signs do repeat themselves so we have our pattern in only one cycle this makes a period of only pi.

b) If we think back to our ratio identities we know that sin is really y/r and cos is x/r we also know that r is always equal to 1 and then we can think about all our other ratios, tan y/x csc r/y ect r is no longer on the bottom, this means that the function isn't restricted to just one. Sin and cos are restricted because they will always be over r and r will always be equal to one, this is also why they have amplitudes of one.