Find the cosine of the angle formed by the complex number in the unit circle

Given a complex number $z = \cos(\theta) + i\sin(\theta)$ on the unit circle, find the cosine of the angle $\theta$.

We know that for a complex number on the unit circle, $z = e^{i\theta} = \cos(\theta) + i\sin(\theta)$.

The real part of $z$ is $\cos(\theta)$.

Therefore, the cosine of the angle $\theta$ is simply the real part of $z$ which is $\cos(\theta)$.

$ \cos(\theta) = \Re(z) $

Given a complex number $z = cos( heta) + isin( heta)$ on the unit circle, find the cosine of the angle $ heta$.

Consider $z = e^{i heta} = cos( heta) + isin( heta)$.

To find the cosine of the angle $ heta$, observe the real part of $z$:

$cos( heta) = Re(z) $

This is the required cosine value, derived directly from the real part of the unit circle representation of $z$.

Given a complex number $z = cos( heta) + isin( heta)$ on the unit circle, find the cosine of the angle $ heta$.

Since $z = e^{i heta}$, the real part of $z$ is $cos( heta)$.

Thus, $cos( heta) = Re(z)$.

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