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Question
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cos A = `(7)/(25)`
Solution
cos A = `(7)/(25)`
cosA = `"Base"/"Hypotenuse" = (7)/(25)`
By Pythagoras theorem, we have
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ Perpendicular = `sqrt(("Hypotenuse")^2 - ("Base")^2`
⇒ Perpendicular
= `sqrt((25)^2 - (7)^2`
= `sqrt(625 - 49)`
= `sqrt(576)`
= 24
sinA = `"Perpendicular"/"Hypotenuse" = (24)/(25)`
tanA = `"Perpendicular"/"Base" = (24)/(7)`
secA = `(1)/"cosA" = (25)/(7)`
cotA = `(1)/"tanA" = (7)/(24)`
cosecA = `(1)/"sinA" = (25)/(24)`.
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