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 30^o = 1/2 and cos pi/6 = cos 30^o = sin 60^o = (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.