Find the sine and cosine values for a given angle on the unit circle
Answer 1
Mia Harris
Suppose we need to find the sine and cosine values for the angle $ \frac{\pi}{4} $ on the unit circle.
Step 1: Recognize the angle $ \frac{\pi}{4} $ on the unit circle.
Step 2: Recall that $ \frac{\pi}{4} $ corresponds to 45 degrees.
Step 3: Know that the coordinates at 45 degrees (or $ \frac{\pi}{4} $ radians) on the unit circle are $ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $.
Step 4: Therefore, $ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $ and $ \cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $.
$ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $
$ \cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $
Answer 2
Matthew Carter
To find the sine and cosine of the angle $ frac{pi}{4} $ on the unit circle, follow these steps:
1. Identify the angle $ frac{pi}{4} $.
2. Recognize that $ frac{pi}{4} $ is equivalent to 45 degrees.
3. The coordinates at $ frac{pi}{4} $ (or 45 degrees) on the unit circle are $ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $.
4. Thus, $ sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $ and $ cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $.
$ sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
Answer 3
Emily Hall
To find the sine and cosine of $ frac{pi}{4} $:
1. $ frac{pi}{4} $ is 45 degrees.
2. Coordinates are $ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $.
Therefore:
$ sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
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