If x is an angle in standard position with point A(-3 , 4) on the terminal side, then sec(x) =

We will draw a line between the point (-3, 4) and the
origin point.

Then angle x located between the line and the
x-axis.

Then, we hace formed a right angle triangle where
the base = 3, the height = 4 .

Now we will calculate the
length of the line which is the hypotenuse.

==> The
hypotenuse = sqrt(3^2 + 4^2 ) = sqrt25 = 5

Now we will
determine sec(x).

We know that sec(x) =
1/cos(x)

But cos(x) = adjacent /
hypotenuse.

==> cos(x) =
3/5

But the angle is in the 4th
quadrant.

then cos(x) =
-3/5

==> sec(x) =
-5/3