Trigonometric graphs are cynical which means they repeat themselves over and over again. One time through their cycle is called a period. The period for sine and cosine is 2pi while the period for tangent and cotangent is pi. The pattern for sine is ++-- (meaning it is positive in the first quadrant and second quadrant while being negative in the third and fourth quadrant) This cycle is one period. It takes one full revolution around the unit circle for this cycle to repeat, so one revolution is 360 degrees or 2pi. This is the same for cosine because its pattern is +--+(meaning it is positive in the first quadrant, negative in the second and third quadrant and positive in the fourth quadrant) and it would take one revolution or 2pi for the cycle to repeat. The period for tangent and cotangent is pi. Tangent's cycle is +-+- . This means it is positive in the first quadrant , negative in the second quadrant, positive in the third quadrant, and negative in the fourth quadrant. Notice that it only takes half the unit circle for its cycle to repeat from positive to negative. Therefore it only takes 180 degrees or pi units to repeat its cycle, making its period pi. The image below gives you a visual of what quadrants the trig functions are positive or negative.
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 amplitude is half the distance between the highest and lowest points on the graph. Sine and cosine have amplitudes of one because based on our knowledge of the unit circle it only goes 1 unit in every direction. So the furthest points it can go to is 1 or -1. So the distance from 1 or -1 to the x axis is 1 unit, making our amplitude 1. Cotangent, tangent, cosecant, and secant do not have amplitudes, however they do have asymptotes. They have asymptotes where sine and cosine equal zero.
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