Find the exact value of if and
We draw the approximate graph of the angle in quadrant III,
since it is between 180° and 270°.
Since , and since ,
we take , the numerator of the cosine and ,
the denominator of the cosine, draw a perpendicular from the terminal
side of to the x-axis, and label the horizontal side
of the resulting triangle , (negative because it goes
to the left), and the hypotenuse . The hypotenuse is
always taken positive:
Now we use the Pythagorean theorem to find the length of
the vertical side:
Since the vertical side of the right triangle goes
down from the x-axis, we label it negative as
Next we want to find .
We use the identity:
We substitute and
Edwin