If `A=(cos150^@`) and `B=(sin60^@)`, then what is `A/B` equal to ?

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

To solve the problem, we need to find the value of \( \frac{A}{B} \) where \( A = \cos 150^\circ \) and \( B = \sin 60^\circ \).

### Step-by-Step Solution:

1. **Identify the values of A and B:**
- \( A = \cos 150^\circ \)
- \( B = \sin 60^\circ \)

2. **Calculate \( A = \cos 150^\circ \):**
- We know that \( 150^\circ \) is in the second quadrant where cosine is negative.
- The reference angle for \( 150^\circ \) is \( 180^\circ - 150^\circ = 30^\circ \).
- Therefore, \( \cos 150^\circ = -\cos 30^\circ \).
- Since \( \cos 30^\circ = \frac{\sqrt{3}}{2} \), we have:
\[ A = \cos 150^\circ = -\frac{\sqrt{3}}{2} \]

3. **Calculate \( B = \sin 60^\circ \):**
- We know that \( \sin 60^\circ = \frac{\sqrt{3}}{2} \).

4. **Calculate \( \frac{A}{B} \):**
- Now we can substitute the values of \( A \) and \( B \):
\[ \frac{A}{B} = \frac{-\frac{\sqrt{3}}{2}}{\frac{\sqrt{3}}{2}} \]
- This simplifies to:
\[ \frac{A}{B} = -1 \]

5. **Final Answer:**
- Therefore, the value of \( \frac{A}{B} \) is \( -1 \).

### Summary:
\[ \frac{A}{B} = -1 \]