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Question
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cosB = `(4)/(5)`
Solution
cosB = `(4)/(5)`
cosB = `"Base"/"Hypotenuse" = (4)/(5)`
By Pythagoras theorem, we have
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ Perpendicular = `sqrt(("Hypotenuse")^2 - ("Base")^2`
⇒ Perpendicular
= `sqrt((5)^2 - (4)^2`
= `sqrt(25 - 16)`
= `sqrt(9)`
= 3
sinB = `"Perpendicular"/"Hypotenuse" = (3)/(4)`
tanB = `"Perpendicular"/"Base" = (3)/(4)`
secB = `(1)/"cosB" = (5)/(4)`
cotB = `(1)/"tanB" = (4)/(3)`
cosecB = `(1)/"sinB" = (5)/(3)`.
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