Inverse Functions Study Guide In this lesson, we introduce
inverse trigonometric functions. With these, we are able to find
the angles of right triangles whose sides are known. When we
plug an angle θ into a trigonometric function like sine, out
comes a ratio r of lengths. The inverse sine (written either
sin–l or arcsin) is a function that does the exact opposite. If
you plug in a ratio r of sides, out will come the corresponding
angle θ. For example, sin(30°) = , so sin–l() = 30°. Similarly,
sin(90°) = 1, so sin–l(l) = 90°. In general, if sin(θ) = r, then
sin–l(r) = θ. Said another way, sin–l(r) = the angle θ for which
sin(θ) = r. The one difficulty that arises is that several
angles can have the same ratio, for example, sin(45°) = and
sin(l35°) = . What should sin–l be? It cannot output two things.
To avoid this problem, it has been decided that only angles –90°
≤ θ ≤ 90° can come out of the sin–l function. Because –90° ≤ 45°
≤ 90° (and 135° is not), we have sin–l = 45°. It might help to
see the graph of y