Find the Cosine Given the Point (9,-12)

Problem

Find *cos(θ)* given the point *(9,−12)

Solution

1. Identify the coordinates of the given point (x,y) on the terminal side of the angle θ

x=9

y=−12

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

r=√(,9+(−12)2)

r=√(,81+144)

r=√(,225)

r=15

3. Apply the definition of the cosine function in terms of x and r

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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