Question

How to solve tan ϑ + 1 = 0 in the domain 0 ≤ ϑ ≤ 3600?

Answer 1

Values of `theta` in the interval `0 <= theta < 3600^@` are

`{135^@,315^@,495^@,675^@,855^@,1035^@,1215^@,1395^@,1575^@,1755^@,1935^@,2115^@,2295^@,2475^@,2655^@,2835^@,3015^@,3195^@,3375^@,3555^@}`

Explanation:

As `tantheta+1=0`, we have

`tantheta=-1=tan((3pi)/4)=tan135^@`

As tangent has a cycle of `180^@`

`theta=180^@xxn+135^@`, where `n` is an integer

and values of `theta` in the interval `0 <= theta < 3600^@` are

`{135^@,315^@,495^@,675^@,855^@,1035^@,1215^@,1395^@,1575^@,1755^@,1935^@,2115^@,2295^@,2475^@,2655^@,2835^@,3015^@,3195^@,3375^@,3555^@}`