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

Problem

cos(θ)* given *(x,y)=(−5,−12)

Solution

1. Identify the coordinates of the point on the terminal side of the angle θ where x=−5 and y=−12

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

r=√(,(−5)2+(−12)2)

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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