Given theta is an acute angle such that sin theta = 5/13 find the value of tan (theta - pi4)

bobbie71G

bobbie71G

Answered question

2020-12-27

Given theta is an acute angle such that sin theta = 513 find the value of tan(θπ/4)

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2020-12-28Added 88 answers

tan(θπ4)=(tanθtan(π4)1+tanθtanπ4)=
tanθ11+tanθ.
In a right triangle with hypotenuse length 13 and a leg length of 5, the other leg has a length 13252=144=12. In this triangle, when sinθ=513 (opp/hyp) then tanθ=oppadj=512.
Therefore tan(θπ4)=51211+512=7121712=717.

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