annotations for full credit. **\#2.) Which angle is coterminal with $$ \frac{3 \pi}{2} $$ ? a) $$ -\frac{3 \pi}{2} $$ b) $$ -\frac{\pi}{2} $$ c) $$ \frac{\pi}{2} $$ d) $$ \frac{5 \pi}{2} $$ (

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UpStudy AI · Accepted Answer

To find an angle that is coterminal with $$ \frac{3 \pi}{2} $$, we can use the property that coterminal angles differ by integer multiples of $$ 2\pi $$. This means we can add or subtract $$ 2\pi $$ (or $$ 360^\circ $$ in degrees) to the given angle.

### Step 1: Identify the given angle
The given angle is:
$$
\theta = \frac{3 \pi}{2}
$$

### Step 2: Find coterminal angles
To find coterminal angles, we can use the formula:
$$
\theta + 2k\pi
$$
where $$ k $$ is any integer.

### Step 3: Calculate coterminal angles
1. For $$ k = 1 $$:
   $$
   \frac{3 \pi}{2} + 2\pi = \frac{3 \pi}{2} + \frac{4 \pi}{2} = \frac{7 \pi}{2}
   $$
2. For $$ k = -1 $$:
   $$
   \frac{3 \pi}{2} - 2\pi = \frac{3 \pi}{2} - \frac{4 \pi}{2} = -\frac{\pi}{2}
   $$

### Step 4: List the options
Now, let's compare the calculated coterminal angles with the provided options:
- a) $$ -\frac{3 \pi}{2} $$
- b) $$ -\frac{\pi}{2} $$ (this is coterminal)
- c) $$ \frac{\pi}{2} $$
- d) $$ \frac{5 \pi}{2} $$

### Conclusion
The angle that is coterminal with $$ \frac{3 \pi}{2} $$ is:
$$
\boxed{-\frac{\pi}{2}}
$$

Thus, the correct answer is option **b)** $$ -\frac{\pi}{2} $$.
The angle coterminal with $$ \frac{3 \pi}{2} $$ is $$ -\frac{\pi}{2} $$.

annotations for full credit.
**#2.) Which angle is coterminal with ?
a)
b)
c)
d)
(

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annotations for full credit. **#2.) Which angle is coterminal with ? a) b) c) d) (