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

Problem

Find *cos(θ)* given the point *(3,−3)

Solution

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

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

r=√(,3+(−3)2)

r=√(,9+9)

r=√(,18)

r=3√(,2)

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

cos(θ)=3/(3√(,2))

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

cos(θ)=1/√(,2)

cos(θ)=√(,2)/2

Final Answer

cos(θ)=√(,2)/2

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