Question

If `tanx= -2/9` and `sinx>0` what are the remaining trigonometric functions?

Answer 1

As below.

Explanation:

`"Given : " tan x = - 2/9`

`tan theta = "(Opp. side) / (Adj. side)" = -2/9`

`"tan is negative in II & IV Quadrants"`

`"Hypotenuse " = sqrt(2^2 + 9^2) = 9.22`

`color(red)(" Case 1 : "`

Values of other trigonometric functions when tan x in II Quadrant :

`cot x = - 9/2`

`sin x = 2/9.22, csc x = 1/ sin x = 4.61`

`cos x = -9 / 9.22, sec x = -9.22 / 9`

`color(blue)(" Case 2 : "`

Values of other trigonometric functions when tan x in IV Quadrant :

`cot x = - 9/2`

`sin x = -2/9.22, csc x = 1/ sin x = -4.61`

`cos x = 9 / 9.22, sec x = 9.22 / 9`