Find the value of $ cos( heta) $ using the unit circle when $ heta = frac{5pi}{4} $
Answer 1
Chloe Evans
To find the value of $ \cos(\theta) $ using the unit circle when $ \theta = \frac{5\pi}{4} $, we first locate this angle on the unit circle.
The angle $ \theta = \frac{5\pi}{4} $ lies in the third quadrant.
We know that $ \theta = \frac{5\pi}{4} $ is equivalent to $ 225^{\circ} $.
In the third quadrant, both sine and cosine are negative.
On the unit circle, the coordinates for $ 225^{\circ} $ are $ (-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}) $.
Therefore, $ \cos(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2} $.
Answer 2
Benjamin Clark
To find the value of $ cos( heta) $ when $ heta = frac{5pi}{4} $ using the unit circle, note that this angle corresponds to $ 225^{circ} $ and lies in the third quadrant.
The coordinates at $ 225^{circ} $ are $ (-frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}) $.
Therefore, $ cos(frac{5pi}{4}) = -frac{sqrt{2}}{2} $.
Answer 3
Isabella Walker
The value of $ cos(frac{5pi}{4}) $ using the unit circle is $ -frac{sqrt{2}}{2} $.
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