Find the Cosine Given the Point (-12,5)

Problem

cos(θ)* given the point *(−12,5)

Solution

1. Identify the coordinates of the given point (x,y) where x=−12 and y=5

2. Calculate the distance r from the origin to the point using the Pythagorean theorem formula r=√(,x2+y2)

r=√(,(−12)2+5)

r=√(,144+25)

r=√(,169)

r=13

3. Apply the formula for the cosine of an angle in standard position, which is cos(θ)=x/r

cos(θ)=(−12)/13

Final Answer

cos(θ)=−12/13

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