# Cosine inverse and cast rule

1. Nov 14, 2012

### chiuda

I am currently doing a trig question and trying to find the location of the acute angles of cosine inverse and I am just wondering if cosine inverse follow the cast rule? In other words would it be positive where cos would be positive or not?

2. Nov 14, 2012

### tiny-tim

hi chiuda!
for acute angles (even for negative ones), cos is always positve

(and cos-1 is usually defined to have its principal value, which is defined to be in [0,π), and therefore is positive anyway)

3. Nov 14, 2012

### chiuda

Related acute angle sorry. If cos is neg then it must be in quadrant 3 or 4.

4. Nov 14, 2012

### chiuda

Right?

5. Nov 15, 2012

### Staff: Mentor

The restricted domain for the cosine function (sometimes written as Cos) is, as tiny-tim said, [0, $\pi$]. This is the range of the inverse cosine function (cos-1). The domain for the inverse cosine function is [-1, 1]. This function maps a number in the interval [-1, 1] to a number in the interval [0, $\pi$]. Except for 0, all the other values are positive.