To go from $\frac{\pi}{4}$ to $\frac{3\pi}{4}$, you can follow these steps:

1. Recognize that $\frac{3\pi}{4}$ is equivalent to adding $\frac{\pi}{2}$ (a quarter-turn on the unit circle) to $\frac{\pi}{4}$: $\frac{\pi}{4} + \frac{\pi}{2} = \frac{3\pi}{4}.$

2. To add the fractions, they must have a common denominator. The least common denominator of 4 and 2 is 4.

   • Rewrite $\frac{\pi}{2}$ with a denominator of 4: $\frac{\pi}{2} = \frac{2\pi}{4}.$

3. Add the fractions: $\frac{\pi}{4} + \frac{2\pi}{4} = \frac{1\pi + 2\pi}{4} = \frac{3\pi}{4}.$

Final Result:

$\frac{\pi}{4} + \frac{\pi}{2} = \frac{3\pi}{4}.$

Would you like further clarification or examples?

---

Related Questions:

1. How do you convert $\frac{\pi}{4}$ to degrees?
2. What is the radian equivalent of $135^\circ$ (equal to $\frac{3\pi}{4}$)?
3. What is $\frac{3\pi}{4} - \frac{\pi}{4}$ and why does it work out as expected?
4. How do you simplify trigonometric expressions involving $\frac{3\pi}{4}$?
5. What is the cosine of $\frac{3\pi}{4}$?

Tip:

Always ensure fractions have a common denominator before adding or subtracting them.