Find the Tangent Given the Point (8,-15)

Problem

(8,−15)

Solution

1. Identify the coordinates of the given point (x,y) where x=8 and y=−15

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

3. Substitute the values into the formula: r=√(,8+(−15)2)=√(,64+225)=√(,289)=17

4. Apply the trigonometric definition for tangent, which is the ratio of the y-coordinate to the x-coordinate: tan(θ)=y/x

5. Calculate the final value by plugging in the coordinates: tan(θ)=(−15)/8

Final Answer

tan(θ)=−15/8

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