The point 512 is on the terminal side of an angle in standar

The point (-5,-12) is on the terminal side of an angle in standard position. Find the cosine value for this angle?

I used pythagorean theorem to find the length of the hypotenese:

a² + b² = c²

(-5)² + (-12)² = c²

25 +144 = c²

169^1/2 = c²

13 = c

Then found the inverse of cosine to isloate the angle

cos = adj/ hyp

cos = -5/13

= cos^-1 (-5/13)

= 112.62 degrees

Is this right?

You have found the hypotunese correctly

But you must notice that the angle lies in the 3rd quardrant

This doesnt change the value of cos(theta). It is still -5/13

However theta would change as theta must lie between 180 to 270 degrees

Hence theta = 247.38 degrees.

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