Principal values of inverse trigonometric functions I have watched multiple times on the videos on inverse cosine and tangent but I couldn't find a relation to these questions below:
Can anyone explain further? 



https://www.khanacademy.org/math/trigonometry/trig-equations-and-identities/inverse-trig-functions/v/inverse-trig-functions-arccos 
https://www.khanacademy.org/math/trigonometry/trig-equations-and-identities/inverse-trig-functions/v/inverse-trig-functions-arctan
 A: If you have a scientific calculator with you, the answers are easy: just enter those expressions and press  or "=". The calculator will give you the principal value of those functions.
If you do not have a calculator, use your knowledge of those functions to make an approximation which will be close enough to choose one of the four offered possibilities.
In the second question, you want the arccosine of a positive number that is less than one. If you visualize the triangles you will see that the resulting angle is between $0°$ and $90°$. In radians this is between $0$ and $\pi/2$. You know that pi is a little larger than three, so that means between $0$ and a little more than $1.5$. Only one of the given possible answers is in that range, so the answer must be $1.25$. And that is what a calculator gives.
In the first question, the number inside the arctangent is positive, so the resulting angle is between $0$ and a little more than $1.5$. The only given possible answer in that range is $1.31$.
Do you need more detail?
