Math problem?

Question

If (theta) is an angle in standard position and the terminal side of theta passes through the point (-5,6), the cos theta =

I have no idea how to do this problem what so ever, it is from the smaple placment test website for umass dartmouth. I don't even remember doing this

If you can explain how to do this problem that would be great :-)

Answer 1

standard position means that the point of the angle is at 0,0 on a set of cartesian coordinates and one side goes along the x axis from x=0 towards positve x.
so if the other leg of the angle goes through a point in the cartesian plane (-5, 6) then you can see that the angle is very obtuse, roughly 130 degrees.
cos of an obtuse angle is negative, corresponding to the span along the negative x axis. so cos theta = - cosine(180-theta)
from the point we can easily find the angle of (180-theta) from the arc tan absolute val of rise/run = arctan 6/5 = 50.2 (so that's 50.2 degrees up from the negative x axis).
and the cosine 50.2 = 0.64
so cos theta = -0.64

Answer 2

Draw the picture.

Left 5. Up 6.

Compute the hypotenuse length. √[(-5)(-5) + (6)(6)]

Cosine of theta = -5/(hypotenuse length).