Understanding the Cosine Inverse Function and the Cast Rule

[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?

 

[tiny-tim]

hi 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?

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)

 

[chiuda]

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

 

[chiuda]

Right?

 

[Mark44]

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

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.