Write the value of sec`30^(@)`.

Options

A. `(2)/(sqrt(3))`
B. `(sqrt(3))/(2)`
C. `(1)/(sqrt(3))`
D. `sqrt(3)`

Answer

To find the value of secant 30 degrees (sec 30°), we can follow these steps:

### Step 1: Understand the definition of secant.
Secant is defined as the reciprocal of cosine. Therefore, we can write:
\[ \sec \theta = \frac{1}{\cos \theta} \]

### Step 2: Write the expression for sec 30°.
Using the definition of secant, we can express sec 30° as:
\[ \sec 30° = \frac{1}{\cos 30°} \]

### Step 3: Find the value of cos 30°.
The value of cos 30° is a known trigonometric ratio:
\[ \cos 30° = \frac{\sqrt{3}}{2} \]

### Step 4: Substitute the value of cos 30° into the secant expression.
Now, substituting the value of cos 30° into the expression for sec 30° gives:
\[ \sec 30° = \frac{1}{\frac{\sqrt{3}}{2}} \]

### Step 5: Simplify the expression.
To simplify \(\frac{1}{\frac{\sqrt{3}}{2}}\), we can multiply by the reciprocal:
\[ \sec 30° = \frac{2}{\sqrt{3}} \]

### Step 6: Rationalize the denominator (optional).
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 \(\sec 30°\) is:
\[ \sec 30° = \frac{2}{\sqrt{3}} \quad \text{or} \quad \frac{2\sqrt{3}}{3} \]

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