If `sin A=3/5` , then the value of sec A is:

Options

A. `4/5`
B. `3/4`
C. `4/3`
D. `5/4`

Answer

To find the value of \( \sec A \) given that \( \sin A = \frac{3}{5} \), we can follow these steps:

### Step 1: Use the Pythagorean Identity
We know from the Pythagorean identity that:
\[ \sin^2 A + \cos^2 A = 1 \]
Given \( \sin A = \frac{3}{5} \), we can square this value:
\[ \sin^2 A = \left(\frac{3}{5}\right)^2 = \frac{9}{25} \]

### Step 2: Substitute into the Identity
Now we substitute \( \sin^2 A \) into the Pythagorean identity:
\[ \frac{9}{25} + \cos^2 A = 1 \]

### Step 3: Solve for \( \cos^2 A \)
To find \( \cos^2 A \), we rearrange the equation:
\[ \cos^2 A = 1 - \frac{9}{25} \]
To perform the subtraction, we need a common denominator:
\[ 1 = \frac{25}{25} \]
Thus,
\[ \cos^2 A = \frac{25}{25} - \frac{9}{25} = \frac{16}{25} \]

### Step 4: Find \( \cos A \)
Now we take the square root of \( \cos^2 A \):
\[ \cos A = \sqrt{\frac{16}{25}} = \frac{4}{5} \]
Since we are considering angles in the first quadrant, \( \cos A \) is positive.

### Step 5: Calculate \( \sec A \)
The secant function is the reciprocal of the cosine function:
\[ \sec A = \frac{1}{\cos A} = \frac{1}{\frac{4}{5}} = \frac{5}{4} \]

### Final Answer
Thus, the value of \( \sec A \) is:
\[ \sec A = \frac{5}{4} \]

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