Cosecant function is an reverse of sine. CSC=(1/sin(x)). In this picture it shows the vertical asymptotic. This first picture is the parent and it shows two period. This range is any real number to -1 and 1 to any real number. It is symmetric to the origin. The hill is its local minimum point. Y=2sec(x) gives the amplitude, The amplitude controls where it starts. This amplitude for this picture is 2,the bigger the number the higher the wave is.The range is undefined to 2. Y=sec(2x) shows the period shift, the range is the same as the first picture. The period shift allows it to be bigger and smaller.Y=sec(x-2) is the horizontal shift allowing it move left or right. The range is still the same. Y=2+sec(x) is the vertical shift and that moves it up and down and that changes the the position but not the range, the range remain the same.