Given the point $P(x, y)$ on the unit circle where $x = -frac{1}{sqrt{2}}$ and $y = -frac{1}{sqrt{2}}$, find the angle $ heta$ in radians.
Answer 1
Chloe Evans
First, recognize that the coordinates given are $x = -\frac{1}{\sqrt{2}}$ and $y = -\frac{1}{\sqrt{2}}$. These values correspond to specific angles on the unit circle. We need to determine where both sine and cosine are negative and equal in magnitude.
Looking at the unit circle, we see that $\theta = \frac{5\pi}{4}$ radians has these properties.
Therefore, the angle $\theta$ in radians is \(\theta = \frac{5\pi}{4}\).
Answer 2
Michael Moore
Given the coordinates $x = -frac{1}{sqrt{2}}$ and $y = -frac{1}{sqrt{2}}$, we need to identify the corresponding angle $ heta$. These coordinates indicate that both sine and cosine are equal and negative. For this to happen, $ heta$ must be located in the third quadrant.
In the third quadrant, the angle with these coordinates is $frac{5pi}{4}$ radians.
Hence, the angle $ heta$ equals ( heta = frac{5pi}{4}).
Answer 3
Christopher Garcia
Given $P(x, y)$ with $x = -frac{1}{sqrt{2}}$ and $y = -frac{1}{sqrt{2}}$, the angle $ heta$ is ( heta = frac{5pi}{4}).
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