How do the trig graphs relate to the Unit Circle?
 |
| Kirch's SSS Packet |
a.) Period?- Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
The period for sine and cosine is 2pi because when you go around the Unit Circle, you have to go around the entire circle in order for the patterns to repeat again. Sine's pattern in the quadrants is positive, positive, negative, negative and we see a pattern. Therefore the period would be 2pi because you had to go around the unit circle an entire time to see the repetition. For cosine the same applies but the pattern is positive, negative, negative positive. And you would also have to go around the unit circle entirely to see the pattern. So basically it takes 1 entire time around the Unit Circle to get repeating patterns for both sine and cosine which is 2 pi.
The period for tangent is pi because you only need to go around the Unit Circle half way to get a repeating pattern. So it would be positive, negative, positive, negative to see a distinct pattern. Half of the unit circle is pi.
b.) Amplitude?- How does the fact that sine and cosine have amplitudes of one (and the other trig functions don’t have amplitudes) relate to what we know about the Unit Circle?
The range of the Unit Circle values is from -1 to 1 so it determines the value of the amptitude. Sine's ratio is y/r and r=1 on the unit circle so you would only be limited to using one. Similarily, cosine's ratio is x/r, where r also equals 1, so you could only use 1 as well. Therefore, both sine and cosine have an amplitude of 1.
No comments:
Post a Comment