Find the Cosine Given the Point (-2,5)

Problem

cos(θ)* given the point *(−2,5)

Solution

1. Identify the coordinates of the given point (x,y) where x=−2 and y=5

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

r=√(,(−2)2+5)

r=√(,4+25)

r=√(,29)

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

cos(θ)=(−2)/√(,29)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,29)

cos(θ)=(−2√(,29))/29

Final Answer

cos(θ)=−(2√(,29))/29

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