Home > Resources > Homework > Math > Unit Circle

Find the angle $ heta $ on the unit circle where the equation $ cos^2( heta) - sin^2( heta) = 1 - 2sin^2( heta) $ holds true

Answer 1

Abigail Nelson

Benjamin Clark

To solve for $ \theta $ on the unit circle in the equation $ \cos^2(\theta) – \sin^2(\theta) = 1 – 2\sin^2(\theta) $, start by using trigonometric identities:

\n

We know that $ \cos^2(\theta) = 1 – \sin^2(\theta) $, so the equation becomes:

\n

$ 1 – \sin^2(\theta) – \sin^2(\theta) = 1 – 2\sin^2(\theta) $

\n

Simplify both sides:

\n

$ 1 – 2\sin^2(\theta) = 1 – 2\sin^2(\theta) $

\n

The equation holds for any $ \theta $ where $ 1 – 2\sin^2(\theta) $ is defined, which simplifies to $ \theta = n\pi $, where $ n $ is an integer.

Answer 2

Alex Thompson

Christopher Garcia

Given $ cos^2( heta) – sin^2( heta) = 1 – 2sin^2( heta) $, we substitute $ cos^2( heta) = 1 – sin^2( heta) $:

$ 1 – sin^2( heta) – sin^2( heta) = 1 – 2sin^2( heta) $

This simplifies to:

$ 1 – 2sin^2( heta) = 1 – 2sin^2( heta) $

Therefore, $ heta = npi $, where $ n $ is an integer.

Answer 3

Amelia Mitchell

Charlotte Davis

From $ cos^2( heta) – sin^2( heta) = 1 – 2sin^2( heta) $, substitute $ cos^2( heta) $:

$ 1 – sin^2( heta) – sin^2( heta) = 1 – 2sin^2( heta) $

This simplifies to:

$ heta = npi $