SOLUTION: If sec X = 3 and the terminal side x does not lie on the first quadrant, find the other circular function values of x.

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Question 1175232: If sec X = 3 and the terminal side x does not lie on the first quadrant, find the
other circular function values of x.

Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!
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

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