Step 1: Let θ = sin^(-1)(3/5). This means sin(θ) = 3/5.
Step 2: To find sec(θ), we first need to find cos(θ). We can use the Pythagorean theorem.
Step 3: In a right triangle, if the opposite side is 3 and the hypotenuse is 5, we can find the adjacent side using the formula: adjacent^2 + opposite^2 = hypotenuse^2.
Step 4: So, adjacent^2 + 3^2 = 5^2. This simplifies to adjacent^2 + 9 = 25.
Step 5: Subtract 9 from both sides: adjacent^2 = 16. Therefore, adjacent = √16 = 4.
Step 6: Now we have the lengths of all sides: opposite = 3, adjacent = 4, hypotenuse = 5.
Step 7: Now we can find cos(θ): cos(θ) = adjacent/hypotenuse = 4/5.
Step 8: Finally, sec(θ) is the reciprocal of cos(θ): sec(θ) = 1/cos(θ) = 5/4.
Step 9: To express sec(θ) in terms of the original problem, we need to find sec(sin^(-1)(3/5)). We already found cos(θ) = 4/5, so sec(θ) = 5/4.
Step 10: To find sec(sin^(-1)(3/5)), we can also use the relationship: sec(θ) = √(1 + tan^2(θ)). We can find tan(θ) = opposite/adjacent = 3/4.
