Question

What is sin 7x/4 ? I need help on this URGENT Trig

Answer 1

If you start from the "standard" sine function, i.e.

$y = \sin(x)$

You can change its graph in four ways:

Amplitude: you can multiply the whole function by a constant to stretch/squeeze it vertically. The transformation looks like

$y = \sin(x) \to y = k\sin(x)$

Phase: you can add a constant to the argument translate it horizontally. The transformation looks like

$y = \sin(x) \to y = \sin(x+k)$

Period: you can multiply the argument by a constant to stretch/squeeze it horizontally. The transformation looks like

$y = \sin(x) \to y = \sin(kx)$

Shift: you can add a constant to the whole function to translate it vertically. The transformation looks like

$y = \sin(x) \to y = \sin(x)+k$

In your case, we're changing the period of the function. If $k>1$ the function is squeezed, so you're squeezing the graph horizontally by a factor of 7/4