Find the sine, cosine, and tangent values for the angle 45° on the unit circle.

To solve for the sine, cosine, and tangent values for the angle $45^{\circ}$ on the unit circle, we use the following properties of the unit circle:

The coordinates for any angle $\theta$ on the unit circle are $(\cos \theta, \sin \theta)$. For $45^{\circ}$, we have:

$\cos 45^{\circ} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

$\sin 45^{\circ} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

To find the tangent value, we use the formula: $\tan \theta = \frac{\sin \theta}{\cos \theta}$ For $45^{\circ}$, we get: $\tan 45^{\circ} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

For the angle $45^{circ}$ on the unit circle, the sine, cosine, and tangent values can be found as follows:

On the unit circle, $cos heta$ and $sin heta$ represent the coordinates $(x,y)$. For $45^{circ}$ the coordinates are:

$cos 45^{circ} = cos left(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

$sin 45^{circ} = sin left(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

To calculate the tangent, we use: $ an heta = frac{sin heta}{cos heta}$ Therefore, for $45^{circ}$: $ an 45^{circ} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$

For $45^{circ}$ on the unit circle:

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

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

$ an 45^{circ} = 1$

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