What is the sine of 45 degrees in the unit circle?

First, we need to remember that the unit circle has a radius of 1 and it is centered at the origin (0,0).

To find the sine of 45 degrees, we use the coordinates of the point where the terminal side of the angle intersects the unit circle.

The angle of 45 degrees is in the first quadrant, and for an angle θ in the unit circle, the coordinates of the point are (cosθ, sinθ).

For 45 degrees, which is π/4 radians, both the cosine and sine values are equal to $ \frac{\sqrt{2}}{2} $.

Therefore, the sine of 45 degrees is:

$ \sin 45^\circ = \frac{\sqrt{2}}{2} $

To find the sine of 45 degrees, we consider the unit circle where the radius is 1.

In the unit circle, the angle 45 degrees corresponds to $ frac{pi}{4} $ radians.

The coordinates of the point on the unit circle at this angle are (cos45°, sin45°).

Since both the sine and cosine of 45 degrees are equal in the unit circle, we have:

$ sin 45^circ = frac{sqrt{2}}{2} $

So, the sine of 45 degrees is:

$ sin 45^circ = frac{sqrt{2}}{2} $

In the unit circle, the sine of 45 degrees is:

$ sin 45^circ = frac{sqrt{2}}{2} $

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