To convert radian measures to degrees, we use the conversion factor: $1 \text{ radian} = \frac{180^\circ}{\pi}$

Given this, we multiply the radian measure by $\frac{180^\circ}{\pi}$ to convert to degrees.

a. $\frac{4\pi}{3}$ radians: $\frac{4\pi}{3} \times \frac{180^\circ}{\pi} = \frac{4 \times 180^\circ}{3} = \frac{720^\circ}{3} = 240^\circ$

b. $\frac{7\pi}{4}$ radians: $\frac{7\pi}{4} \times \frac{180^\circ}{\pi} = \frac{7 \times 180^\circ}{4} = \frac{1260^\circ}{4} = 315^\circ$

c. $\frac{\pi}{2}$ radians: $\frac{\pi}{2} \times \frac{180^\circ}{\pi} = \frac{180^\circ}{2} = 90^\circ$

d. $-\frac{3\pi}{4}$ radians: $-\frac{3\pi}{4} \times \frac{180^\circ}{\pi} = -\frac{3 \times 180^\circ}{4} = -\frac{540^\circ}{4} = -135^\circ$

e. $-\frac{2\pi}{3}$ radians: $-\frac{2\pi}{3} \times \frac{180^\circ}{\pi} = -\frac{2 \times 180^\circ}{3} = -\frac{360^\circ}{3} = -120^\circ$

So the conversions are:

• $\frac{4\pi}{3}$ radians = $240^\circ$
• $\frac{7\pi}{4}$ radians = $315^\circ$
• $\frac{\pi}{2}$ radians = $90^\circ$
• $-\frac{3\pi}{4}$ radians = $-135^\circ$
• $-\frac{2\pi}{3}$ radians = $-120^\circ$

Would you like any further details or explanations?

Here are some related questions:

1. How do you convert degrees to radians?
2. What is the formula for converting between degrees and radians?
3. How can you use the unit circle to understand radian measures?
4. What are some common angles and their radian equivalents?
5. Why are radians often used in calculus and higher mathematics?
6. How do you add and subtract angles in radians?
7. What is the significance of $\pi$ in trigonometry?
8. How do you graph angles in radians on the coordinate plane?

Tip: Always remember that $\pi$ radians is equal to $180^\circ$. This can help quickly convert between degrees and radians.