Double Whammy

Geometry Level 2

What is the fundamental period of the function f ( x ) = ∣ sin ⁡ ( x ) ∣ + ∣ cos ⁡ ( x ) ∣ f(x) = | \sin(x) | + | \cos(x) | ?

π \pi π 4 \frac \pi 4 π 2 \frac \pi 2 2 π 2 \pi

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Shubhadeep Nandy by Shubhadeep Nandy , 23, India

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2 solutions

Kenny Lau
Aug 7, 2015

f ( x + π / 2 ) = ∣ sin ⁡ ( x + π / 2 ) ∣ + ∣ cos ⁡ ( x + π / 2 ) ∣ = ∣ cos ⁡ x ∣ + ∣ sin ⁡ x ∣ = f ( x ) f(x+\pi/2)=|\sin(x+\pi/2)|+|\cos(x+\pi/2)|=|\cos x|+|\sin x|=f(x)

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Hadia Qadir
Jul 31, 2015

pie/2 exceptional case... coz on adding pie/2 in either o the functions sine will change in cosine and vise versa

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