Find the Cosine Given the Point (3,-4)

Problem

Find *cos(θ)* given the point *(3,−4)

Solution

1. Identify the coordinates of the given point (x,y) where x=3 and y=−4

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

r=√(,3+(−4)2)

r=√(,9+16)

r=√(,25)

r=5

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

cos(θ)=3/5

Final Answer

cos(θ)=3/5

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