if tan theta = 3/2 and sin <0, find the values of all six of the trig functions?

If tanθ = 3/2 > 0 and sinθ < 0, then
θ is in quadrant III,
sinθ = (-3)/√(2^2 + 3^2) = -3/√13.

Since tanθ = 3/2,
2sinθ = 3cosθ
cosθ = 2/3 * sinθ.
Since sinθ = -3/√13,
cosθ = 2/3 * (-3)/√13 = -2/√13 and
cscθ = 1/sinθ = -√(13)/3.

Since cosθ = -2/√13,
secθ = 1/cosθ = -√(13)/2.

Since tanθ = 3/2,
cotθ = 1/tanθ = 2/3.

I call x is angel subsitute for theta, srr. provided that tanx < 0 , cosx > 0 . So x in quadrant 4 that mean sine < 0 so now, draw a triangle with adjoining =a million, hypotenuse = 3 . locate the different = sqrt ( 3^2 -a million ) = sqrt( 8) sinx = - sqrt(8)/ 3 tan x = - sqrt(8) i wish this help ya. you are able to locate different trig function by skill of your self like sec, csc, cot by skill of receprocal of different function corresponding with them.