Find the equation of the line tangent to the graph of y = sin^-1 (x/5) at x = 5/2. Show your work.

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

Simplify:

We can factor out the denominator within the square root:

Simplify:

So, we can find the slope of the tangent line at x = 5/2. By substitution:

Evaluate:

We will also need the point at x = 5/2. Using our original equation, we acquire that:

So, the point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

Distribute:

Isolate. Hence, our equation is:

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