# Determining the period of a trigonometric function

ainster31

## Homework Statement

$$f(x)=sin2x+cos4x$$

## The Attempt at a Solution

$$The\quad period\quad of\quad sin2x\quad is\quad π.\quad The\quad period\quad of\quad cos4x\quad is\quad \frac { π }{ 2 } .\\ \\ What\quad is\quad the\quad period\quad of\quad f(x)?$$

Tanya Sharma

## Homework Statement

$$f(x)=sin2x+cos4x$$

## The Attempt at a Solution

$$The\quad period\quad of\quad sin2x\quad is\quad π.\quad The\quad period\quad of\quad cos4x\quad is\quad \frac { π }{ 2 } .\\ \\ What\quad is\quad the\quad period\quad of\quad f(x)?$$

What is the lowest common multiple of the periods of sin2x and cos4x ?

Homework Helper
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Suppose you have two periods, p_1 and p_2
the COMMON period must then satisfy n*p_1=m*p_2, for integers n and m to be determined.

That is, the common period must be, as Tanya Sharma says, a COMMON MULTIPLE of the two periods, and the LEAST one at that.

ainster31
How does that work considering that cos is sin but displaced on the x-axis?

According to this graph, T=pi is wrong:

ainster31
Never mind.

I'm an idiot. You're right.

Thanks.