Find the Cosine Given the Point (14,-14)

Problem

Find *cos(θ)* given the point *(14,−14)

Solution

1. Identify the coordinates of the given point (x,y) where x=14 and y=−14

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

r=√(,14+(−14)2)

r=√(,196+196)

r=√(,392)

r=14√(,2)

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

cos(θ)=14/(14√(,2))

4. Simplify the fraction by canceling the common factor of 14 and rationalizing the denominator.

cos(θ)=1/√(,2)

cos(θ)=√(,2)/2

Final Answer

cos(θ)=√(,2)/2

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