Math Snap

STEP 1

1. We are comparing radian measures to determine which is the largest.
2. The options provided are in terms of $\pi$, which is a common unit in trigonometry.
3. We will compare the numerical values of the given radian measures.

STEP 2

1. Simplify each radian measure.
2. Compare the simplified radian measures.
3. Determine the largest radian measure.

STEP 3

Simplify each radian measure:
a) $\frac{12 \pi}{9}$ simplifies to $\frac{4 \pi}{3}$ by dividing the numerator and the denominator by 3.
b) "None of the above" is not a radian measure and will be considered only if no other option is larger.
c) $\frac{3 \pi}{2}$ is already in its simplest form.
d) $\frac{7 \pi}{4}$ is already in its simplest form.

STEP 4

Compare the simplified radian measures:
- $\frac{4 \pi}{3}$ is approximately $4.18879$ (using $\pi \approx 3.14159$).
- $\frac{3 \pi}{2}$ is approximately $4.71239$.
- $\frac{7 \pi}{4}$ is approximately $5.49779$.

Determine the largest radian measure:
- Comparing the values, $\frac{7 \pi}{4}$ is the largest.
The largest radian measure is option d) $\frac{7 \pi}{4}$.
The answer is $\boxed{d}$.