"The terminal ray of angle β , drawn in standard position, passes through the point (−4, 3√5) .
What is the value of cosβ ?"
This puts the angle in the second quadrant so cosβ will be negative.
Imagine a right angled triangle where the hypotenuse reaches from the origin to the point.
Then the length of the hypotenuse is given by sqrt((-4)2 + (3√5)2) = √61
Hence cosβ = -4/√61 or cosβ = -4√61/61