$Identify the cosine and sine values of 45° using the unit circle$

To find the cosine and sine values of 45° using the unit circle, we first recognize that 45° corresponds to the angle π/4 radians.

In the unit circle, the coordinates of the point where the terminal side of the angle intersects the circle provide the cosine and sine values.

At 45° (π/4), both the x-coordinate (cosine) and y-coordinate (sine) are equal. They are both equal to 1/√2, which simplifies to √2/2.

Therefore, for 45°:

$\cos(45°) = \frac{\sqrt{2}}{2}$

$\sin(45°) = \frac{\sqrt{2}}{2}$

To determine the cosine and sine values for 45° on the unit circle, we convert the degree to radians, which is π/4.

On the unit circle, the coordinates at π/4 are equally divided.

Since the unit circle has a radius of 1, the coordinates (x, y) are:

$left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

Thus, the values are:

$cos(45°) = frac{sqrt{2}}{2}$

$sin(45°) = frac{sqrt{2}}{2}$

Using the unit circle, the angle 45° (or π/4 radians) has coordinates:

$left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

So,

$cos(45°) = frac{sqrt{2}}{2}$

$sin(45°) = frac{sqrt{2}}{2}$

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