Find the angles at which $ sin( heta) = cos( heta) $

To find the angles where $ \sin(\theta) = \cos(\theta) $, we know that:

$ \sin(\theta) = \cos(\theta) $

Dividing both sides by $ \cos(\theta) $, we get:

$ \tan(\theta) = 1 $

Thus, $ \theta $ must be an angle where the tangent is 1. We know that $ \tan(\theta) = 1 $ at:

$ \theta = \frac{\pi}{4} + n\pi $

where $ n $ is any integer. So, the angles are:

$ \theta = \frac{\pi}{4}, \frac{5\pi}{4}, \frac{9\pi}{4}, … $

To solve for $ heta $ in $ sin( heta) = cos( heta) $:

$ sin( heta) = cos( heta) $

Divide by $ cos( heta) $ to get:

$ an( heta) = 1 $

This happens at:

$ heta = frac{pi}{4} + npi $

for integer $ n $. Therefore, the angles are:

$ heta = frac{pi}{4}, frac{5pi}{4}, frac{9pi}{4}, … $

We need to find angles $ heta $ where $ sin( heta) = cos( heta) $:

$ an( heta) = 1 $

This occurs at:

$ heta = frac{pi}{4} + npi $

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