Find the Tangent Given the Point (24,-7)

Problem

(24,−7)

Solution

1. Identify the coordinates of the given point (x,y) where x=24 and y=−7

2. Calculate the radius r of the circle passing through the origin and the point using the Pythagorean theorem r=√(,x2+y2)

r=√(,24+(−7)2)

r=√(,576+49)

r=√(,625)=25

3. Apply the formula for the tangent function in terms of coordinates, which is tan(θ)=y/x

tan(θ)=(−7)/24

Final Answer

tan(θ)=−7/24

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