## Sine Cosine Pythagorean Identity

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

### Sine Cosine Pythagorean Identity

I am currently learning about Verifying trigonometric identities and it has been a really long time since I have taken any algebra. I wanted to know if I could modify the pythagorean identity to such:

So, the sine, cosine pythagorean identity is:

$\sin ^{2}\theta + \cos ^{2}\theta = 1$

so that means that this is also true:

$\cos ^{2}\theta = 1 - \sin^{2}\theta$

or...

$\cos ^{2}\theta = -\sin^{2}\theta + 1$

So here is my question. I don't remember if I am allowed to do this but does that mean that this can also be true? -->

$-\cos ^{2}\theta = \sin^{2}\theta - 1$

eliotmason

Posts: 3
Joined: Tue Oct 29, 2013 5:36 am

### Re: Sine Cosine Pythagorean Identity

eliotmason wrote:$\sin ^{2}\theta + \cos ^{2}\theta = 1$

so that means that this is also true:

$\cos ^{2}\theta = 1 - \sin^{2}\theta$

$\cos ^{2}\theta = -\sin^{2}\theta + 1$

does that mean that this can also be true? --> $-\cos ^{2}\theta = \sin^{2}\theta - 1$

Yes:
-1(cos^2(@)) = -1(-sin^2(@) + 1
-cos^2(@) = +sin^2(@) - 1