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

Problem

(−7,24)

Solution

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

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

r=√(,(−7)2+24)

r=√(,49+576)

r=√(,625)=25

3. Apply the formula for the tangent of the angle θ formed by the point in standard position, which is defined as tan(θ)=y/x

tan(θ)=24/(−7)

4. Simplify the fraction by moving the negative sign to the numerator.

tan(θ)=−24/7

Final Answer

tan(θ)=−24/7

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