If you have a funciton of Y=SinX and you change it to Y=Sin(BX, where B is any integer how is the graph affect

Question

specifcally the period and phase shift. Please explain it in a mathmatical way

Answer 1

no phase shift, but the period becomes 2pi/B (or 360/B if you're using degrees) and all the x's values are divided by B. This could be a horizontal shrink (abs value of B>1) or a stretch (-1

Answer 2

it will affect the period of the graph..meaning the cycle of the sin curve will either be faster or slower. for example, sin2x will make the sin curve cycle faster (one complete cycle between 0 and pi vs 0 and 2 pi) and sin(x/2) would make the curve cycle slower (one comlete cycle between 0 and 4 pi)

Answer 3

it affects the frequency of the curve and also it's period. the frequency is the number of waves in every 2pi interval. the "B" in the equation actually corresponds to the graph's frequency. and it's period is 2pi/frequency... you could also look at it as though it's the wavelength of the graph(the distance from peak to peak).

Answer 4

If |B| > 1, Y=sin(bx) will have a shorter period than Y=sin(x).

Sin(x) repeats over a 2pi cycle. Sin(2x) repeats over a 1pi cycle since when x = pi, 2x = 2pi.

If 0< |B| < 1, Y=sin(bx) will have a longer period than y=sin(x).

Sin(x) repeats over a 2pi cycle. Sin(.5x) repeats over a 4pi cycle since when x=4i, .5x = 2pi.

Answer 5

it affects the period because the period is equal to 2 over the interger of the x