Question

$if \cos(a) = \frac{1}{3} find all trignometric ratios$
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Answer 1

cos (a) = 1/3

let adjacent side be x.

then hypotenuse = 3x

and opposite side = √ (3x)^2 - (x^2)

= √ (9x^2) - (x^2)

= √ (8x^2)

= x√8

sin(a) = opposite/hypotenuse

= (x√8)/(3x)

= √8/3

tan (a) = sin(a)/cos(a)

= √8/3 ÷ 1/3

= √8/3 × 3

= √8

cosec (a) = 1/sin(a)

= 3/√8

sec(a) = 1/cos (a)

= 3

cot (a) = 1/tan(a)

= 1/√8