Quick Math Question

Why is acos(1.5) an error? Isn't that just asking how many radians it takes to reach 1.5 degrees around a circle?

No it is not asking changing radians to degrees

 

acos is the same as inverse cos.

It is saying  if    \(cos\theta =1.5 \text{ then what is }\theta\)

 

Well the cos of any angle must be between -1 and +1

1.5 is outside this range so the question does not make sense.

 

If you want to know how many radians in 1.5 degrees then think of it like this

 

\(360^\circ=2\pi ^c \\ 180^\circ=\pi ^c \\ 1^\circ=(\frac{\pi}{180})^c\\ 1.5^\circ=(\frac{1.5*\pi}{180})^c\\ 1.5\;degrees=\frac{\pi}{120}\;radians\\ \)

Adding to what Melody said:

Radians are a measure of the arc length. Cosine is a measure of horizontal distance that an angle produces in a circle with radius = 1.