### Home > CALC > Chapter 7 > Lesson 7.3.3 > Problem7-134

7-134.

Find the equation of a line tangent to the graph of $f(x) =\operatorname{arcsin} x$ at $x =\frac { 1 } { 2 }$.

1. Use the tangent line to find an approximate value of $f(0.52)$.

Because $y =\operatorname{arcsin}(0.52)$ is hard to evaluate, the tangent line at $x = 0.52$ will give a decent approximation of $f(0.52)$.

2. Is your approximation an over or under estimate? Use the second derivative to justify your answer.

That will indicate if the tangent line is above or below the graph.