Question

Find all the solutions of sin^2 3x- sin^2 x=0
on the interval [0,2pi)

Answer 1

Are you sure it is sin^2 (3x) ?

Answer 2

Yup, it's all together.

Answer 3

Then maybe the second term is also sin^2 (3x)
Please check.

Answer 4

Nope. That's what it says on the paper. I separated the 3x so it wouldn't seem as if it was part of the exponent.

Answer 5

Then you will have to make a substitution for sin^2 (3x)

Answer 6

How?O.o

Answer 7

sin^2 (3x) = sin^2 (x)
3x=x or 3x=-x mod pi

Answer 8

3x=x or 3x=-x mod pi
2x=0 or 4x=0 mod pi
x=n*pi/4, where n is an integer

Answer 9

x={0, pi/4, pi/2, 3pi/4, pi, 5pi/4, 3pi/2, 7pi/4}

Answer 10

(pi is the period of sin^2(x); sin^2(-x)=sin^2(x))

Answer 11

Thank you so much!:) So, what does mod mean?

Answer 12

mod allows variables to take on multiple values
x mod 10, for example, is the set {...x-30,x-20,x-10,x,x+10,x+20,x+30,...}
the equations 3x=x or 3x=-x are taken modulus pi since sin^2(x+pi)=sin^2(x)
this way, all values of x satisfying that equation sin^2 (3x) = sin^2 (x) will be found

Answer 13

https://www.khanacademy.org/math/applied-math/cryptography/modarithmetic/a/what-is-modular-arithmetic