Find the values of $ an( heta) $ for $ heta $ in the unit circle at $ 0 $, $ frac{pi}{4} $, $ frac{pi}{3} $, and $ frac{pi}{2} $

To determine the values of $ \tan(\theta) $ for $ \theta $ in the unit circle at $ 0 $, $ \frac{\pi}{4} $, $ \frac{\pi}{3} $, and $ \frac{\pi}{2} $, we evaluate the tangent function at these angles:

For $ \theta = 0 $:

$ \tan(0) = 0 $

For $ \theta = \frac{\pi}{4} $:

$ \tan\left(\frac{\pi}{4}\right) = 1 $

For $ \theta = \frac{\pi}{3} $:

$ \tan\left(\frac{\pi}{3}\right) = \sqrt{3} $

For $ \theta = \frac{\pi}{2} $:

$ \tan\left(\frac{\pi}{2}\right) = \text{undefined} $

We need to calculate the tangent values for $ 0 $, $ frac{pi}{4} $, $ frac{pi}{3} $, and $ frac{pi}{2} $:

For $ heta = 0 $:

$ an(0) = 0 $

For $ heta = frac{pi}{4} $:

$ anleft(frac{pi}{4}
ight) = 1 $

For $ heta = frac{pi}{3} $:

$ anleft(frac{pi}{3}
ight) = sqrt{3} $

For $ heta = frac{pi}{2} $:

$ anleft(frac{pi}{2}
ight) = ext{undefined} $

Calculate $ an( heta) $ at:

$ an(0) = 0 $

$ anleft(frac{pi}{4}
ight) = 1 $

$ anleft(frac{pi}{3}
ight) = sqrt{3} $

$ anleft(frac{pi}{2}
ight) = ext{undefined} $

Start Using PopAi Today