The terminal ray of angle β , drawn in standard position, passes through the point (−4, 3√5) .

"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