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

1 Answer
Shwetank Mauria
Apr 29, 2017

Values of thetaθ in the interval 0 <= theta < 3600^@0≤θ<3600∘ are

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

Explanation:

As tantheta+1=0tanθ+1=0, we have

tantheta=-1=tan((3pi)/4)=tan135^@tanθ=−1=tan(3π4)=tan135∘

As tangent has a cycle of 180^@180∘

theta=180^@xxn+135^@θ=180∘×n+135∘, where nn is an integer

and values of thetaθ in the interval 0 <= theta < 3600^@0≤θ<3600∘ are

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

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