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Question
Given: cos A = 0.6; find all other trigonometrical ratios for angle A.
Solution
Consider the diagram below:
cos A = 0 . 6
cos A = `(6)/(10 ) = (3)/ (5)`
i .e. `" base " /"hypotenuse" = 3/5 ⇒ "AB " / "AC " = 3/5 `
Therefore if length of AB = 3x, length of AC = 5x
Since
AB2 + BC2 = AC2 ...[ Using Pythagoras Theorem ]
(3x)2 + BC2 = (5x)2
BC2 = 25x2 - 9x2 = 16x2
∴ BC = 4x ...( perpendicular )
Now all other trigonometric ratios are
sin A = `"perpendicular"/"hypotenuse" = (4x)/(5x) = 4/5`
cosec A = ` "hypotenuse" / " perpendicular" = "AC"/ "BC" = (5x) / (4x) = 5/4`
sec A = `" hypotenuse" / " Base " = "AC"/"AB" = ( 5x)/(3x) = 5/3`
tan A = `"perpendicular"/ " base" = (4x)/(3x) = 4/3 `
cot A = `"base"/"perpendicular" = (3x)/(4x) = 3/4`
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