The coodinates are (-0.8968 , -0.4425). Please see the details of this problem.?

Question

Find the angle in radians between 0 and 2*(3.14) determined by terminal points of the unit circle. Round your answer to the hundreths.

I don't understand on how to do the problem. My answer key shows me 3.6. I need help on how they came up with this answer.

Answer 1

It's often handy to draw yourself out a little sketch. From it you can see the location of the given point.

To identify the angle the given point makes with the x-axis and the y-axis use trigonometry. Switch to radians.
tan Θ = opp./ adj.
Θ = tan^-1 opp./ adj.
Θ = tan^-1 (-0∙4425./ -0∙8968)
Θ = tan^-1 (-0∙493 210 52)
Θ = 0∙458 370 613 rad.
This is the value of the angle below the x-axis. You need to include the angle above the x-axis, which is 180º or π radians.
Θ = 0∙458 370 613 rad. + π rad.
Θ = (0∙458 370 613 + 3∙14) rad.
Θ = 3∙598 370 613 rad.
Θ ≈ 3∙6 rad.

Answer 2

That's right. The point is in the third quadrant. 180 degrees offset is arctang(0.4425/0.8968) = 26.2627 degrees. If you add it to 180 degrees it is 206.2627 degrees. Since there are 360/2pi degrees in one radian it is (206.2627/360)*2pi = 3.6 radians.

Answer 3

The point is in the 3rd quadrant (-x,-y), so
-0.4425/-0.9868 = tan(θ - π)
θ - π = 0.421538498
θ = 3.56313 ≈ 3.6