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

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We have that x is an angle in standard position with point A(-3 , 4) on the terminal side.

sec x = 1/ cos x

cos x = adjacent side / hypotenuse.

Here the adjacent side is -3 and the hypotenuse is sqrt ((-3^2) + 4^2) = sqrt ( 9 + 16) = sqrt 25 = 5.

The value of cos x = -3/5

**Therefore the required value of sec x is -5/3**

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**

The terminal point A has the coordinates (-3, 4).

Let O be the origin whose coordinates are (0,0).

x is the angle the point OA makes with x axis positive direction.

Therefore OA = sqrt{(-3-0)^2+(4-0)^2)} = 5.

Let the feet of perpendicular from A to x axis be X.

Then OX = -3, XA = 4.

Then angle AOX = x.

Therefore secant x = hypotenuse/ (adj side to angle x) = OA/OX

= 5/(-3) = -5/3.

**So sec(x) = -5/3**.