We have a conflict of notation. We can't call the x-axis if we call the angle
x also. So I will call the angle capital X and the x-axis by small x.
If sec X = 3 and the terminal side x does not lie on the first quadrant, find the
other circular function values of x.
We will consider 3 as the fraction 3/1.
Since the secant is positive in the first and fourth quadrant and it does not
lie in the first quadrant, then it lies in the fourth quadrant.
We draw a right triangle with an angle in Q4, and remember that the secant
is the hypotenuse over the adjacent (or the r over the x). So we put the
numerator of 3/1, which is 3, on the hypotenuse (or the r) and the denominator
of 3/1, which is 1, on the adjacent side, (or the x). Then we calculate the
opposite side (or the y) by using the Pythagorean theorem:
_
Since it's Q4 we know that y is negative, so we put -2√2 on the opposite
side (y):
So now we know that
Edwin
