Finding the $sin$, $cos$, and $ an$ of $45^circ$ using the unit circle

To find the trigonometric functions of $45^\circ$ using the unit circle, note that $45^\circ$ corresponds to an angle in the first quadrant where both the x and y coordinates are equal.

Since the radius of the unit circle is 1, the coordinates of the point on the circle at $45^\circ$ are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.

Thus:

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

$ \cos(45^\circ) = \frac{\sqrt{2}}{2} $

$ \tan(45^\circ) = 1 $

To determine the values of $sin$, $cos$, and $ an$ at $45^circ$ using the unit circle, we use the known coordinates $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$:

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

$ cos(45^circ) = frac{sqrt{2}}{2} $

$ an(45^circ) = 1 $

Using the unit circle, at $45^circ$, coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$:

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

$ cos(45^circ) = frac{sqrt{2}}{2} $

$ an(45^circ) = 1 $

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