No, $\sin \frac{\pi}{4}$ does not equal 2.

To understand this, let's go through the details:

1. The value of $\sin \frac{\pi}{2}$ is indeed 1, as you mentioned. This is a special angle in trigonometry where the sine of 90 degrees (or $\frac{\pi}{2}$ radians) equals 1.

2. However, $\sin \frac{\pi}{4}$ (which is the sine of 45 degrees) does not equal 2. Instead: $\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2} \approx 0.707$

This is because the sine function has a maximum value of 1 for real numbers, meaning it cannot exceed 1. So $\sin \frac{\pi}{4} = 2$ is impossible within real-valued trigonometry.

Would you like more details on the properties of the sine function or other trigonometric identities?

Here are five related questions that might interest you:

1. What is the value of $\sin \frac{\pi}{6}$?
2. Why is the maximum value of the sine function 1?
3. How do we derive $\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$?
4. What is the relationship between $\sin$ and $\cos$ for complementary angles?
5. What are other common angles with known sine values?

Tip: Remember, the sine function oscillates between -1 and 1, so it can never reach values beyond these limits for real inputs.