Find the Cosine Given the Point (-1,-3)

Problem

cos(θ)* given the point *(−1,−3)

Solution

1. Identify the coordinates of the given point (x,y) where x=−1 and y=−3

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

r=√(,(−1)2+(−3)2)

r=√(,1+9)

r=√(,10)

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

cos(θ)=(−1)/√(,10)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,10)

cos(θ)=−√(,10)/10

Final Answer

cos(θ)=−√(,10)/10

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