Determine the exact values of sine and cosine for the angle $ frac{pi}{4} $ using the unit circle
Answer 1
Matthew Carter
To find the exact values of sine and cosine for the angle $ \frac{\pi}{4} $, we use the unit circle.
For $ \theta = \frac{\pi}{4} $, the coordinates on the unit circle are:
$ ( \cos( \frac{\pi}{4} ), \sin( \frac{\pi}{4} )) $
Since $ \frac{\pi}{4} $ is an angle in the first quadrant where sine and cosine values are positive, we use the 45-degree reference angle values. We have:
$ \cos( \frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
$ \sin( \frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
Thus, the exact values are:
$ \cos( \frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
$ \sin( \frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
Answer 2
Alex Thompson
To find the exact values of sine and cosine for the angle $ frac{pi}{4} $, we use the unit circle.
For $ heta = frac{pi}{4} $, the coordinates on the unit circle are:
$ ( cos( frac{pi}{4} ), sin( frac{pi}{4} )) $
Since $ frac{pi}{4} $ is an angle in the first quadrant, we have:
$ cos( frac{pi}{4}) = frac{sqrt{2}}{2} $
$ sin( frac{pi}{4}) = frac{sqrt{2}}{2} $
Answer 3
Ella Lewis
To find the exact values of sine and cosine for the angle $ frac{pi}{4} $:
For $ heta = frac{pi}{4} $, we have:
$ cos( frac{pi}{4}) = frac{sqrt{2}}{2} $
$ sin( frac{pi}{4}) = frac{sqrt{2}}{2} $
Start Using PopAi Today