Find the Tangent Given the Point (5,-12)

Problem

(5,−12)

Solution

1. Identify the coordinates of the given point (x,y) as x=5 and y=−12

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

3. Calculate the radius value:

r=√(,5+(−12)2)

r=√(,25+144)

r=√(,169)=13

4. Apply the trigonometric definition for tangent, which is the ratio of the ycoordinate to the xcoordinate.

tan(θ)=y/x

5. Substitute the values x=5 and y=−12 into the formula.

tan(θ)=(−12)/5

Final Answer

tan(θ)=−12/5

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