Find the Cosine Given the Point (6,-7)

Problem

cos(θ)* given the point *(6,−7)

Solution

1. Identify the coordinates of the given point (x,y) where x=6 and y=−7

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

r=√(,6+(−7)2)

r=√(,36+49)

r=√(,85)

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

cos(θ)=6/√(,85)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,85)

cos(θ)=(6√(,85))/85

Final Answer

cos(θ)=(6√(,85))/85

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