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Question
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cose C = `(15)/(11)`
Solution
cose C = `(15)/(11)`
cose C = `(1)/"sin C" ="Hypotenuse"/"Perpendicular" = (15)/(11)`
By Pythagoras theorem, we have
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ Base = `sqrt(("Hypotenuse")^2 - ("Perpendicular")^2`
⇒ Base
= `sqrt((15)^2 + (11)^2`
= `sqrt(225 - 121)`
= `sqrt(104)`
sin C = `"Perpendicular"/"Hypotenuse" = (11)/(15)`
cos C = `"Base"/"Hypotenuse" = sqrt(104)/(11)`
tan C = `"Perpendicular"/"Base" = (11)/sqrt(104)`
sec C = `(1)/"cos C" = (15)/(sqrt(104)`
cot C = `(1)/"tan A" = sqrt(104)/(11)`.
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