Determine the value of $sin$, $cos$, and $ an$ for the angle $ heta = frac{pi}{4}$ using the unit circle

Given the angle $\theta = \frac{\pi}{4}$, the corresponding coordinates on the unit circle are:

$ (\cos(\theta), \sin(\theta)) = \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) $

Thus,

$ \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $

$ \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $

The tangent function is the ratio of sine to cosine:

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

For the angle $ heta = frac{pi}{4}$ on the unit circle:

$ cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

$ sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

And the tangent is:

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

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

$ cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

$ sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

And:

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

Start Using PopAi Today