express tan(-235) as a function of a positive acute angle.
Draw the angle in standard position. Since it is negative it is a
clockwise rotation about the origin from the right side of the x-axis,
as indicated by the green arrow
Now we draw the reference angle, which the acute angle, NOT in standard
position which between the terminal side of -255° and the x-axis. I will
indicate the reference angle by a red arc:
Even though the angle -235° is negative it represents an amount of
rotation of +235° and the reference angle is the amount of rotation
more than 180° in the clockwise direction. So we can calculate the
reference angle by subtracting 180° from 235° and 235°-180° = 55°.
However the tangent of referent angle 55° is positive, whereas the
angle -235° is in the second quadrant, so tan(-235°) is a negative
number, so the answer must be negative, so
tan(-235°) = -tan(55°)
Edwin
