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

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Answer 1 · 2018-05-06T04:10:11

As below.

#"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#