well the trig graphs relate to the unit circle because we are still using the unit circle but it is now in a line this time and you still have the quadrants there but its just different it practically everything the same in the unit circle just that we don't use the degrees as an x-axis because when you put it in your graphing calculator you wont be able to see the whole thing of what you want only a little bit of it so that's why we use radians instead but everything else relates to the unit circle.
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 that is how long it takes to repeat it, their pattern doesn't repeat after four marks. On the unit circle the quadrant angles are (0,90,180,270, 360) but we like to do (0, pi/2, pi, 3pi/2, and 2pi) because as i told you its better that way when it comes to plugging it in the calculator you can actually see a snap shot of it that is good enough. Sine is positive in quadrant 1 and quadrant 2, and negative in quadrant 3 and 4 which makes the pattern (+ + - -). Cosine is positive in quadrant 1 and quadrant 4, and negative in quadrant 2 and 3 which makes the pattern (+ - - +). When you see it on the unit circle the pattern for these two trig functions repeats only after one full revolution and since one revolution around the unit circle is 360 degrees it has a period of 2pi. If it was one period on a graph it's like saying one revolution on the unit circle.
http://www.mathwarehouse.com/trigonometry/systems-sine-cosine-functions/images/picture-system-sinex-cosx.gif
Tangent and Cotangent have a period of pi because their pattern of being positive or negative only repeats after two marks or half of a revolution. Tangent is positive in quadrant 1 and 3 and negative in quadrant 2 and 4. Cotangent is the same which means that both of the patterns are (+ - + -). When it comes to putting it on the graph you can notice after every two marks that tangent repeats.
http://etc.usf.edu/clipart/36700/36731/tancotan_36731_lg.gif
sine and cosine have amplitudes of one because sine and cosine have restrictions that can't be greater than 1 or less than -1 so that is where the lowest point (-1) and the highest point (1) should be in the graph, relating to using the unit circle when sine=0 it should equal to one by using the ratio of sine to find out that it is one and when you do cos=0 that should equal to -1. Tangent and the rest of the trig functions do have an assymptote so when the functions are graphed in between the asymptotes the vertex indicates where the function begins to go up to infinity or down to negative infinity.
http://www.teacherschoice.com.au/Maths_Library/Functions/sine_function.gif
source: http://www.education.com/study-help/article/pre-calculus-help-other-trig-functions/
Works Cited Page
sine and cosine
Tangent and Cotangent
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