How to draw the graph of a trigonometry function?
Question:
Draw graph of f(x) = cos x + Sqrt (3) sin x
Solution:
- f(x) = cos x + Sqrt (3) sin x
- = (2/2) [cos x + Sqrt (3) sin x]
- = 2 {(1/2) cos x + [Sqrt (3)/2] sin x}
- note: sin pi/6 = sin 30o = 1/2 and cos pi/6 = cos 30o = sin 60o = Sqrt (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.