The trig graphs relate to the Unit Circle because it uses the negative and positive values of the quadrants in order to define how a period/graph will look for a certain trig function. Each trig function forms a different looking graph. To begin the unit circle unfolds into a line. As we can see above the signs in parenthesis are the values that that quadrant would have on the unit circle (positive or negative). Since we unfolded the unit circle for the sine graph we are left with positive and on the left and negative on the right. This means that our graph will look like an uphill then a down hill. For the cosine we see an uphill, downhill, and then uphill again because of the positive, negative, negative, and positive value on the quadrants when we unfolded the Unit circle. Tangent/cotangent both have an uphill and downhill because they have a shorter period due to the positive and negative on the first two quadrants and positive negative in the third and fourth quadrant.
-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 it takes four quadrants to repeat the same pattern over and over again. Tangent and cotangent has a period of pi because since it already has a positive and a negative value on the first two quadrants it only takes pi to repeat the pattern.
-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 fact that sine and cosine have amplitudes of one relates to what we know about the unit circle because sine and cosine cannot be bigger that one. Since sine and cosine has a ratio of y/r and x/r and r =1. Sine and cosine can only be between -1 and 1.
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