Question

Given: cos A = 0.6; find all other trigonometrical ratios for angle A.

Answer 1

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`