Find the Tangent Given the Point (-3,-4)

Problem

(−3,−4)

Solution

1. Identify the goal, which is to find the value of the tangent function for an angle θ whose terminal side passes through the point (x,y)=(−3,−4)

2. Recall the trigonometric definition of tangent in terms of coordinates on the Cartesian plane.

3. Apply the formula for tangent, which is the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

4. Substitute the given values x=−3 and y=−4 into the formula.

tan(θ)=(−4)/(−3)

5. Simplify the fraction by canceling the negative signs.

tan(θ)=4/3

Final Answer

tan(θ)=4/3

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