Does the Pythagorean Identity Hold for sin^2(3x) + cos^2(3x)?

[AMan24]

Homework Statement

sin²x + cos²x = 1

but would sin²3x + cos²3x = 1?

Homework Equations

none.

The Attempt at a Solution

[/B]
I'm pretty sure sin²3x + cos²3x can't equal 1 otherwise the identity would probably be written as sin²cx + cos²cx = 1 and I've never seen it written like this.

I was doing a homework problem and i ended up in a situation where, if i could use sin²cx + cos²cx = 1, i'd get my answer. But I am doing it differently than the book, so my way might be wrong

 

[phyzguy]

When you write \sin^2(x) + \cos^2(x) = 1 are there restrictions on the values x can take? For example, could x = 3 * y?

 

[AMan24]

no there are no restrictions, so that must mean it does work, or actually, you said x = 3y. I am not sure... there's no restrictions I am aware of

 

[phyzguy]

no there are no restrictions, so that must mean it does work, or actually, you said x = 3y. I am not sure... there's no restrictions I am aware of

Right. It's true for any value of x.

 

[Ray Vickson]

Homework Statement

sin²x + cos²x = 1

but would sin²3x + cos²3x = 1?

Homework Equations

none.

The Attempt at a Solution

[/B]
I'm pretty sure sin²3x + cos²3x can't equal 1 otherwise the identity would probably be written as sin²cx + cos²cx = 1 and I've never seen it written like this.

I was doing a homework problem and i ended up in a situation where, if i could use sin²cx + cos²cx = 1, i'd get my answer. But I am doing it differently than the book, so my way might be wrong

Take $x=10$. Would you agree that $\sin^2 10 + \cos^2 10 = 1?$ Do you really think that makes $\sin^2 30 + \cos^2 30$ come out different from 1? What about $\sin^2 37 + \cos^2 37?$ That would be $\sin^2 cx + \cos^2 cx$ with $c = 3.7$.