Find the Cosine Given the Point (6,8)

Problem

Find *cos(θ)* given the point *(6,8)

Solution

1. Identify the coordinates of the given point (x,y) where x=6 and y=8

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

r=√(,6+8)

r=√(,36+64)

r=√(,100)

r=10

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

cos(θ)=6/10

4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2

cos(θ)=3/5

Final Answer

cos(θ)=3/5

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