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

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Answer 1 · 2017-04-29T06:38:40

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

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

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

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