Barrons AP Calculus

(a)

(b)

(c)

(d)

The period  of  f   is   ,  or  6.

Since   the maximum value   of  −sin    x   is  −(−1)   or  +1, the maximum value   of  f   is

3   +   1   or  4.

    equals  +1  when     ,  that    is, when     .  Solving yields  

.

We  graph    :

Figure  N1–6

D2. Inverses

We obtain inverses of the trigonometric functions by limiting the domains of the
latter so each trigonometric function is one-to-one over its restricted domain. For
example, we restrict

Inverse trig    functions

The graphs of f (x) = sin x on and of its inverse f −1(x) = sin−1x are shown

in Figure N1–7. The inverse trigonometric function sin−1x is also commonly
denoted by arcsin x, which denotes the angle whose sine is x. The graph of sin−1x
is, of course, the reflection of the graph of sin x in the line y = x.