What is the value of sin pi/4?

To calculate the value of $\sin \left(\frac{\pi}{4}\right)$, we can refer to the unit circle or the special triangles that define the trigonometric functions for specific angles. In this case, the angle $\frac{\pi}{4}$ radians is equivalent to 45 degrees, which is one of the angles in a 45-45-90 right triangle.

In a 45-45-90 triangle, the sides are in the ratio of $1:1:\sqrt{2}$, where the hypotenuse is $\sqrt{2}$ times the length of each of the other two sides, which are equal. Since the sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse, we can use this information to find the sine of 45 degrees or $\frac{\pi}{4}$ radians.

For a 45-45-90 triangle, if we let the length of the sides opposite the 45-degree angles be 1, then the hypotenuse will be $\sqrt{2}$. Therefore, the sine of 45 degrees or $\frac{\pi}{4}$ radians is:

$$
\sin \left(\frac{\pi}{4}\right) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{1}{\sqrt{2}}
$$

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{2}$:

$$
\sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}
$$

Thus, the value of $\sin \left(\frac{\pi}{4}\right)$ is $\frac{\sqrt{2}}{2}$.