Math Is Fun Forum

amberzak

Member

Registered: 2012-03-16

Posts: 80

Unit Circle Pythagorean Identities

I'm finishing my essay on the Unit Circle, and I just have a really quick question if someone could oblige.

The pythagorian identities in the unit circle state that, for example, cos^2 theta + sin^2 theta = 1. Does this work when you move all the way around the circle (for example, when the angle is 90 degrees, the triangle in the circle is just a line, so cos will be 0)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Unit Circle Pythagorean Identities

hi amberzak,

Yes, this identity is true for all theta (even beyond 360).

eg. If theta = 135, then sin theta = (root 2) / 2 and cos theta = minus (root 2) / 2

Then when you square these, the minus goes and you have 2 / 4 + 2 / 4 = 1 same as if theta = 45.

Since sine and cosine take the same values in the other quadrants if you ignore the minus signs this will happen for all theta.

Can write this out in a formal proof if you want.

Bob

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amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Unit Circle Pythagorean Identities

No, thats perfect thanks. I wrote that it's always true and I just wanted to make sure what I wrote was accurate. Thanks

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Don't think outside the box. Think there is no box