# The Sin Family

### Jivonni Johnson

The equation Y=sin(x) can be written in different ways. As long as you keep sin you can change the way the graph is. The first picture explains the parent and has a given table with it explaining 5 points on the graph containing 2 periods. The range is -1<x less than or equal too 1. The second picture shows the amplitude, Y=5sin(x), which is the number before sin. It does not have a +/- between it& the range is -5<x less than or equal too 5. The third picture, Y=sin(5x), shows the period shift. To find the period shift you have to divide 2pi over b(the number in the parenthesis with x).It controls whether the the line shrink or lengthens. The range is -1<x less than or equal too 1. The 4th picture is, Y=sin(x-5), shows the horizontal shift. The horizontal shift allows it to move left and right while the period is the same. The range remains -1<x less than or equal too 1. Lastly, 5th picture shows Y=5+sin(x), Vertical shift. Vertical shift allows it to move up or down on the Y-axis.It is located before the amplitude with a +/- separating it.