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How to draw the graph of a trigonometry function?

Question:

Draw graph of f(x) = cos x + square root of three times sin x.

Solution:

f(x) = cos x + (square root of 3) sin x
= (2/2) [cos x + (square root of 3) sin x]
= 2 {(1/2) cos x + [(square root of 3)/2] sin x}
note: sin pi/6 = sin 30o = 1/2 and cos pi/6 = cos 30o = sin 60o = (square root of 3)/2
so, f(x) = 2 (sin pi/6 cos x + cos pi/6 sin x)
use formula: sin (a + b) = sin a cos b + cos a sin b
so, f(x) = 2 sin (pi/6 + x)
f(x) = 2 sin (x + pi/6)
Step 1: draw the graph of f1(x) = 2 sin x
Step 2: shift the graph of f1(x) = 2 sin x toward left pi/6 units to get the graph of f(x) = 2 sin (x + pi/6)
Please watch the video for detail solution.