If angle θ is a principal angle that lies in quadrant 3 such that 0° ≤ θ ≤ 360°, determine the exact values of x, y, and r for tanθ=2/3.

Answer 1

If θ is between 0 and 360 degrees, in the 3rd quadrant, it is between 180 and 270 degrees.

If tan θ = 2/3 (to find θ, just find the tan^-1 2/3)

θ = tan^-1 (2/3)

θ = 33.69°; θ = 33.69° + n(180°); For the 3rd quadrant, you would just add 180°. So

θ = 213.69°

Answer 2

tan x= sin x/cos x

opp./hyp /adj/hyp

opp/adj=2/3

applying the Pythagorean theorem,

Hypotenuse or r=sqrt. of 13 , x=--3, y=-2