Find the sine of the angle located at (45^circ) on the unit circle.
Answer 1
Maria Rodriguez
For an angle of 45 degrees (or \(\frac{\pi}{4}\) radians) on the unit circle, we need to find the sine value.
On the unit circle, the coordinates for an angle \(\theta\) are given by \((\cos(\theta), \sin(\theta))\). For \(\theta = 45^\circ\), the coordinates are \(\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)\).
Therefore, the sine of 45 degrees is:
$\sin(45^\circ) = \frac{\sqrt{2}}{2}$
Answer 2
Michael Moore
To find the sine of 45 degrees, we use the unit circle. The angle 45 degrees is equivalent to (frac{pi}{4}) radians.
On the unit circle, the coordinates corresponding to (45^circ) are (left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)).
The y-coordinate of this point gives us the sine value:
$sin(45^circ) = frac{sqrt{2}}{2}$
Answer 3
Mia Harris
At 45 degrees (or (frac{pi}{4}) radians) on the unit circle, the sine value is the y-coordinate:
$sin(45^circ) = frac{sqrt{2}}{2}$
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