# Math Help - Find the max value of a trigonometric function

1. ## Find the max value of a trigonometric function

Find the maximum value of the function $f(x) =sin^3x-sin^2x+sinx-1$

2. ## Re: Find the max value of a trigonometric function

Let $z = \sin x$ where $-1 \le z \le 1$, so that we want to maximize

$z^3 - z^2 + z - 1$

Then $\frac{d}{dz} = 3z^2 - 2z + 1$

The maximum value occurs either where $d/dz = 0$ or at $z = \pm 1$ Solving $d/dz = 0$ we have two non-real solutions, so the maximum occurs at either -1 or +1. Plugging in we see that z = sin x = 1 works, and the maximum value is 0.