What is the value of sec`330^(@)` ?

Options

A. 2
B. `(-2)/(sqrt(3))`
C. `-2`
D. `(2)/(sqrt(3))`

Answer

To find the value of sec 330°, we can follow these steps:

### Step 1: Rewrite sec 330° in terms of a related angle
We can express 330° as:
\[ 330° = 360° - 30° \]

### Step 2: Use the property of secant
Using the property of secant, we know that:
\[ \sec(360° - \theta) = \sec(\theta) \]
Thus, we can rewrite sec 330° as:
\[ \sec(330°) = \sec(360° - 30°) = \sec(30°) \]

### Step 3: Find the value of sec 30°
Now, we need to find the value of sec 30°. We know that:
\[ \sec(\theta) = \frac{1}{\cos(\theta)} \]
For 30°, the cosine value is:
\[ \cos(30°) = \frac{\sqrt{3}}{2} \]
Therefore:
\[ \sec(30°) = \frac{1}{\cos(30°)} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} \]

### Step 4: Simplify the value
To express sec 30° in a more standard form, we can rationalize the denominator:
\[ \sec(30°) = \frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3} \]

### Final Answer
Thus, the value of sec 330° is:
\[ \sec(330°) = \frac{2\sqrt{3}}{3} \]

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