Point P(-2, -7) is on the terminal arm of an angle  in standard position. Determine the measure of  to the nearest degree.

Answer 1

(-2,-7) is in quadrant 3 where the angles are between 180 and 270 degrees

180<A< 270

reference angle for (2,7) is tan^-1(7/2) = about about 74.055 degrees

in quadrant 3, that's 180+74.055 =about 254.055 degrees

=about 254 degrees

it might help to plot the point and construct a right triangle with sides -2, -7 and hypotenuse = sqr(4+49) = sqr53 = about 7.3

tanA = -7/-2 = 3.5

A = tan^-1(3.5)=about 74 degrees in quadrant 1,

but = about 254 degrees in quadrant 3