Find the Cosine Given the Point (9,12)

Problem

cos(θ)* given *(9,12)

Solution

1. Identify the coordinates of the given point (x,y) where x=9 and y=12

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

r=√(,9+12)

r=√(,81+144)

r=√(,225)

r=15

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

cos(θ)=9/15

4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3

cos(θ)=3/5

Final Answer

cos(θ)=3/5

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