Find the sine, cosine, and tangent of a point on the unit circle

For the point on the unit circle corresponding to the angle $\theta = \frac{\pi}{4}$, find the sine, cosine, and tangent.

Step 1: Recognize that on the unit circle, the radius is 1.

Step 2: Use the angle $\theta = \frac{\pi}{4}$.

Step 3: Find sine and cosine for $\frac{\pi}{4}$. Since $\frac{\pi}{4} = 45^\circ$, $\sin \left( \frac{\pi}{4} \right) = \cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$.

Step 4: Calculate tangent using $\tan \theta = \frac{\sin \theta}{\cos \theta} = 1$.

Answers:

$\sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$

$\cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$

$\tan \left( \frac{\pi}{4} \right) = 1$

For the point on the unit circle corresponding to the angle $ heta = frac{pi}{4}$, determine the sine, cosine, and tangent.

Step 1: Recall that the radius of the unit circle is 1.

Step 2: The chosen angle is $ heta = frac{pi}{4}$.

Step 3: Determine sine and cosine values at $frac{pi}{4}$, knowing that $frac{pi}{4} = 45^circ$ gives $sin left( frac{pi}{4}
ight) = cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$.

Step 4: Compute tangent: $ an heta = frac{sin heta}{cos heta} = 1$.

Solutions:

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

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

$ an left( frac{pi}{4}
ight) = 1$

For the point on the unit circle corresponding to the angle $ heta = frac{pi}{4}$, find the sine, cosine, and tangent.

Using $ heta = frac{pi}{4}$, we have:

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

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

$ an left( frac{pi}{4}
ight) = 1$

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