InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the principal value of each of the following: i) `cos^(-1)(-1/sqrt(2))`, ii) `cos^(-1)(-1/2)`, iii) `cot^(-1)(-1/sqrt(3))` |
|
Answer» i) We know that the range of the principal value of `cos^(-1)` is `[0,pi]`. Let `cos^(-1)(-1/sqrt(2))=theta`. Then, `costheta=-1/sqrt(2)=-cospi/4=cos(pi-pi/4)=cos(3pi)/4`. `therefore theta=(3pi)/4 in [0, pi]`. Hence, the principal value of `cos^(-1)(-1/sqrt(2))` is `(3pi)/4`. ii) We know that the range of the principal value of `cos^(-1)` is `[0,pi]`. Let `cos^(-1)(-1/2)=theta`. Then, `costheta=-1/2=-cospi/3=cos(pi-pi/3)=cos""(2pi)/3`. iii) We know that the range of the principal value of `cot^(-1)` is `(0,pi)`. Let `cot^(-1)(-1/sqrt(3))=theta`. Then, `cottheta=-1/sqrt(3)=-cotpi/3=cot(pi-pi/3)=cot(2pi)/3`. `therefore theta=(2pi)/3 in (0,pi)`. Hence, the principal value of `cot^(-1)(-1/sqrt(3))` is `(2pi)/3.` |
|