Find the Cosine Given the Point (12,16)

Problem

cos(θ)* given *(x,y)=(12,16)

Solution

1. Identify the coordinates of the given point as x=12 and y=16

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

r=√(,12+16)

r=√(,144+256)

r=√(,400)

r=20

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

cos(θ)=12/20

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

cos(θ)=3/5

Final Answer

cos(θ)=3/5

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