Find the sine, cosine, and tangent of an angle of $45^circ$ on the unit circle.

To find the sine, cosine, and tangent of an angle of 45 degrees on the unit circle:

The coordinates of the point at $45^\circ$ on the unit circle are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.
Therefore, $\sin(45^\circ) = \frac{\sqrt{2}}{2}$ and $\cos(45^\circ) = \frac{\sqrt{2}}{2}$.

To find $\tan(45^\circ)$, we use the formula $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$.
Thus, $\tan(45^\circ) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.

To determine the values of sine, cosine, and tangent for $45^circ$ on the unit circle:

The coordinates at $45^circ$ are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Therefore, $sin(45^circ)$ is $frac{sqrt{2}}{2}$ and $cos(45^circ)$ is $frac{sqrt{2}}{2}$.

For tangent, using $ an( heta) = frac{sin( heta)}{cos( heta)}$,
we have $ an(45^circ) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$.

At $45^circ$ on the unit circle, the coordinates are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

So, $sin(45^circ) = frac{sqrt{2}}{2}$, $cos(45^circ) = frac{sqrt{2}}{2}$, and $ an(45^circ) = 1$.

Start Using PopAi Today