How to find the value of inverse Cosine?

Question

The problem is Cos^-1 (-1)
In my book, it solves like this

Let v = Cost^-1 (-1)
Then cos v = -1 and 0
But what i don't get is where did they get the pi answer. Where did the pi come from?

Another problem is Cos^-1 0 = pi/2
Again, where pi/2 comes from?

If someone could help me clarify this, it would help me a lot.
Thanks

Answer 1

If cos(θ) = x, then arccos(x) = θ.
cos^-1(θ) is just another way to say arccos(θ).

v = cos^-1(-1) = arccos(-1)
cos(v) = -1
v = π

v = cos^-1(0) = arccos(0)
cos(v) = 0
v = π/2

Answer 2

PI and PI/2 here are angles expressed in radians instead of degrees. There are 2*PI radians in a circle (360 degrees), so PI = 180 degrees and PI/2 = 90 degrees.

Answer 3

Question 1
let y = cos^(-1) (-1)
cos y = = - 1
cosy is - ve (2nd quadrant)
y = π (check using calculator)
y = cos^(-1) (-1) = π

Question 2
Let y = cos^(-1) (0)
cos y = 0
y = π/2 , y = 3π/2 (check using calculator)
y = cos^(-1) (0) = π/2 , 3π/2