A ∈ QIII, B ∈ QI find
.
First we draw the two angles, A, B, in their respective quadrants:
Draw perpendiculars to the x-axis from the end of the terminal sides of
the angles, creating right triangles.
For angle A:
. Since the adjacent side, x, goes left
on the x-axis, and the opposite side, y, goes downward from the x-axis, we must
consider the tangent as and put the numerator of ,
which is -2, on the y=OPPOSITE side and the denominator of , which is
-3, on the x=ADJACENT SIDE.
For angle B:
Since is in QI we can leave everything positive.
We put the numerator of 3/1, which is 3, on the r=HYPOTENUSE and the denominator
of 3/1, which is 1, on the x=ADJACENT SIDE.
Then we calculate the third sides of the two right triangles by using the
Pythagorean theorem:
for angle A: for angle B:
Now we are able to substitute in
and
Rationalizing the denominator:
Edwin