Period of Sine and Cosine

We know that the base function of sine and cosine goes from 0 - 360 degrees. When we change the period of the function, we are changing how long/short the function is before it repeats itself again. So instead of going from 0 - 360, they would be going from 0 - some other number.

We know that a change in amplitude can be found be y = 2sinx where the 2 in front of the sin shows how high the new function goes. For a change in period, the number is instead directly in front of the x, such as y = sin2x. To get the new period, we know that 360 = 2pi. Divide 2pi by whatever is next to the x: in my example, it would be 2pi/2. The pi is left over, so pi would be our new period. We would much rather work in degrees than radians, so convert pi to degrees by multiplying by 180/pi. The pi's cancel, and you have 180 degrees left. Thus, 180 degrees is the new period of pi. The function still starts at zero, still ends at zero, and still has the same shape, but it becomes only half as long as before. The same rules apply for cosine functions, too!

Note that the amplitude doesn't change if there is no number in front of the trig function. Our function still goes from [-1, 1], but now, it just repeats itself more often because it's period is shorter.