Find the Tangent Given the Point (-6,8)

Problem

(−6,8)

Solution

1. Identify the coordinates of the given point as x=−6 and y=8

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

r=√(,(−6)2+8)

r=√(,36+64)

r=√(,100)=10

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

tan(θ)=8/(−6)

4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

tan(θ)=−4/3

Final Answer

tan(θ)=−4/3

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