# Period of sin4(x) + cos4(x): Find the Answer Here

• phymatter
In summary, the conversation is about finding the period of sin4(x) + cos4(x). The individual periods of sin(x) and cos(x) are both pi, but the period of their sum cannot be found using the LCM method. Instead, it can be found by re-expressing the function using Euler's formula and simplifying. The resulting period is pi/2.
phymatter
i have to find the period of sin4(x) + cos4(x)

i know that the period of both the functions individually is pi , but i am unable to find the period of sum of these two functions..

pl. help!

sin4(x) + cos4(x)=(sin2x+cos2x)2-2sin2x cos2x=2-1\2 sin2(2x).

losiu99 said:
sin4(x) + cos4(x)=(sin2x+cos2x)2-2sin2x cos2x=2-1\2 sin2(2x).

by this we get the period as pi/2 , and that's correct ,
but why can't we get this answer by finding the lcm of the period of two functions?
by that we get ans as pi!

Why should that give the period?

phymatter said:
finding the lcm of the period of two functions

This gives a multiple of the period.

One way to find the period is by re-expressing the function with Euler's formula and then simplify and re-express it back into a trigonometric function.

Period of the function is pi/2

Last edited:

## What is the period of sin4(x) + cos4(x)?

The period of sin4(x) + cos4(x) is 2π.

## How do you find the period of sin4(x) + cos4(x)?

The period of sin4(x) + cos4(x) can be found by finding the period of both sin4(x) and cos4(x), which is 2π, and taking the least common multiple of the two periods, which is also 2π. Therefore, the period of sin4(x) + cos4(x) is 2π.

## What is the range of sin4(x) + cos4(x)?

The range of sin4(x) + cos4(x) is [-1, 1].

## How do you find the range of sin4(x) + cos4(x)?

The range of sin4(x) + cos4(x) can be found by considering the maximum and minimum values of both sin4(x) and cos4(x). Since the maximum value of both functions is 1 and the minimum value is -1, the range of sin4(x) + cos4(x) is [-1, 1].

## What is the graph of sin4(x) + cos4(x)?

The graph of sin4(x) + cos4(x) is a sinusoidal wave with an amplitude of 1, centered at the x-axis, and repeating every 2π units.

• General Math
Replies
33
Views
2K
• General Math
Replies
5
Views
967
• General Math
Replies
3
Views
851
• General Math
Replies
7
Views
1K
• General Math
Replies
2
Views
1K
• General Math
Replies
51
Views
3K
• General Math
Replies
2
Views
1K
• General Math
Replies
6
Views
2K
• General Math
Replies
6
Views
2K
• General Math
Replies
1
Views
1K