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

Problem

Find *cos(θ)* given the point *(−5,12)

Solution

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

2. Calculate the radius r using the distance formula r=√(,x2+y2)

r=√(,(−5)2+12)

r=√(,25+144)

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)=(−5)/13

Final Answer

cos(θ)=−5/13

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