Function

Geometry Level 3

What is the minimum value of P > 0 P>0 , such that when the graph f ( x ) = sin x + cos x f (x) = \sin x + \cos x is shifted left by P P units, we get the graph y = cos x sin x y = \cos x- \sin x ?

π 18 \frac\pi{18} π 2 \frac\pi2 π 4 \frac\pi4 π 6 \frac\pi6

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1 solution

Nicole Ling
Jan 9, 2016

The function of f(x)=sinx+cosx= (2^1/2) sin(x+ π/4 ) , y=cosx - sinx= (2^1/2) sin(x+ 3π / 4 ), so the function move to left in the minimum units of π/ 2 ,so the minimum number of P should be π/2 .

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