# How do you graph  y= ((sqrt 3/2)sin(x)) + (.5cos(x))?

Mar 25, 2018

The given equation

$y = \left(\left(\frac{\sqrt{3}}{2}\right) \sin \left(x\right)\right) + \left(.5 \cos \left(x\right)\right)$

=> y= cos(pi/6)sin(x) + sin(pi/6)cos(x))

$\implies y = 1 \cdot \sin \left(x + \frac{\pi}{6}\right)$
The above relation obviously is a periodic sine function of $x$with amplitude $1$ and initial phase angle $\phi = \frac{\pi}{6}$

so the graph will be as follows