Question

If cotθ =40/9 , find the values of cosecθ and sinθ.

Answer 1

cot A = 40 / 9

=> B /P = 40 / 9

let base = 40a

Perpendicular = 9a

Hypotenuse = sqrt [ (40a)^2 + (9a)^2]

= sqrt ( 1600a^2 + 81a^2)

= sqrt (1681a^2)

= 41a

Now,

Cosec A = H / P

= 41a/ 9a

= 41/ 9
______________

sin A = 1/ cosec A

= 9 / 41

Answer 2

Solution :

Here I am using A instead of theta.

Given cot A = 40/9

i ) Cosec² A = 1 + cot² A

= 1 + ( 40/9 )²

= 1 + 1600/81

= 1681/81

Cosec A = √ 1681/81

cosecA = 41/9

ii ) sin A = 1/cosecA

=> SinA = 1/(41/9)

SinA = 9/41

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