How Are The Fundamental Periods Related?

Geometry Level 2

The fundamental period of sin ⁡ x \sin x is 2 π 2 \pi .
The fundamental period of cos ⁡ x \cos x is 2 π 2 \pi .

What is the fundamental period of sin ⁡ x cos ⁡ x \sin x \cos x ?

π \pi 2 π 2 \pi 3 π 3 \pi 4 π 4 \pi

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Franz Pabilona by Franz Pabilona , 21, Philippines

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2 solutions

Vignesh S
Apr 25, 2016

Relevant wiki: Trigonometric Graphs - Amplitude and Periodicity

sin ⁡ x cos ⁡ x = 0.5 sin ⁡ 2 x \sin{x}\cos{x}=0.5\sin{2x} . Also we see that sin ⁡ 2 ( x + π ) = sin ⁡ 2 x + 2 π = sin ⁡ 2 x \sin{2(x+π)}=\sin{2x+2π}=\sin{2x} . ⟹ \implies the period of the above function is π \color{#D61F06}{\boxed{π}}

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Wow. You're So Smart

Franz Pabilona - 5 years, 1 month ago

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Thanks for the compliment

Vignesh S - 5 years, 1 month ago

Cal me confused but how do you jump from sin x cos x to 0.5 sin 2x ?

Patrick Rannou - 11 months, 4 weeks ago

sin ⁡ ( x ) cos ⁡ ( x ) = sin ⁡ ( 2 x ) 2 \sin(x)\cos(x)=\dfrac{\sin(2x)}{2} . Fundamental period of sin ⁡ ( x ) \sin(x) is 2 π 2\pi .

Therefore Fundamental Period of sin ⁡ ( 2 x ) 2 \dfrac{\sin(2x)}{2} is π \boxed {\pi} .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Wow. You're So Smart.

Franz Pabilona - 5 years, 1 month ago

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