What are the coordinates of the point on the unit circle corresponding to an angle of $45^circ$?
Answer 1
John Anderson
To determine the coordinates of the point on the unit circle at $45^\circ$, we use the fact that the unit circle has a radius of 1 and the coordinates are given by $ (\cos \theta, \sin \theta) $.
For $\theta = 45^\circ$, we have:
$\cos 45^\circ = \frac{\sqrt{2}}{2}$
$\sin 45^\circ = \frac{\sqrt{2}}{2}$
Therefore, the coordinates are:
$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $
Answer 2
Benjamin Clark
To find the coordinates for an angle of $45^circ$ on the unit circle, remember that the unit circle is defined by the equation $ x^2 + y^2 = 1 $. The coordinates can be expressed as $ (cos heta, sin heta) $.
For $ heta = 45^circ$:
$cos 45^circ = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$
$sin 45^circ = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$
Thus, the coordinates are:
$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
Answer 3
Henry Green
On the unit circle, the coordinates corresponding to an angle of $45^circ$ are given by $ (cos heta, sin heta) $.
For $ heta = 45^circ$:
$cos 45^circ = frac{sqrt{2}}{2}$
$sin 45^circ = frac{sqrt{2}}{2}$
Therefore, the coordinates are:
$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
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