Determine the $cos$ and $sin$ values for an angle of $45^circ$ on the unit circle.
Answer 1
Isabella Walker
To determine the $\cos$ and $\sin$ values for an angle of $45^\circ$ on the unit circle, follow these steps:
1. Convert the angle from degrees to radians: $45^\circ = \frac{\pi}{4}$ radians.
2. On the unit circle, the coordinates of a point corresponding to an angle of $\frac{\pi}{4}$ radians are given by $(\cos(\frac{\pi}{4}), \sin(\frac{\pi}{4}))$.
3. Using trigonometric values, we know:
$\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
$\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
Thus, the cosine and sine values for an angle of $45^\circ$ are $\frac{\sqrt{2}}{2}$ and $\frac{\sqrt{2}}{2}$ respectively.
Answer 2
Joseph Robinson
To find the $cos$ and $sin$ values for an angle of $45^circ$ on the unit circle, follow these steps:
1. Convert $45^circ$ to radians, which is $frac{pi}{4}$ radians.
2. On the unit circle, the coordinates of the point at $frac{pi}{4}$ radians are given by $(cos(frac{pi}{4}), sin(frac{pi}{4}))$.
3. We know that:
$cos(frac{pi}{4}) = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$
$sin(frac{pi}{4}) = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$
Therefore, the cosine and sine values at $45^circ$ are $frac{sqrt{2}}{2}$ and $frac{sqrt{2}}{2}$ respectively.
Answer 3
Samuel Scott
For an angle of $45^circ$ on the unit circle:
1. Convert to radians: $45^circ = frac{pi}{4}$.
2. Coordinates at $frac{pi}{4}$ radians are:
$cos(frac{pi}{4}) = frac{sqrt{2}}{2}$
$sin(frac{pi}{4}) = frac{sqrt{2}}{2}$
Thus, the $cos$ and $sin$ values are both $frac{sqrt{2}}{2}$.
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