Evaluate the following
` sec ( cos^(-1) ( 2/3))`.

Answer

To evaluate the expression \( \sec(\cos^{-1}(2/3)) \), we can follow these steps:

### Step 1: Set up the equation
Let \( x = \cos^{-1}(2/3) \). This means that \( \cos(x) = \frac{2}{3} \).

### Step 2: Use the relationship between secant and cosine
We know that \( \sec(x) = \frac{1}{\cos(x)} \). Therefore, we can express \( \sec(x) \) in terms of \( \cos(x) \).

### Step 3: Substitute the value of cosine
Substituting \( \cos(x) = \frac{2}{3} \) into the secant formula, we have:
\[ \sec(x) = \frac{1}{\cos(x)} = \frac{1}{\frac{2}{3}}. \]

### Step 4: Simplify the expression
Now, simplify \( \frac{1}{\frac{2}{3}} \):
\[ \sec(x) = \frac{1 \cdot 3}{2} = \frac{3}{2}. \]

### Step 5: Conclusion
Thus, the value of \( \sec(\cos^{-1}(2/3)) \) is:
\[ \sec(\cos^{-1}(2/3)) = \frac{3}{2}. \]