Question

determine whether the following statement makes sense or does not make sense, and explain your reasoning. i am given that tan θ = 4/3, so i can conclude that y = 4 and x = 3. choose the correct answer below. a. the statement does not make sense because the sign of the tangent function depends on the quadrant in which the angle lies. as the quadrant changes the sign of x changes and the sign of y remains the same. b. the statement does not make sense because the sign of the tangent function depends on the quadrant in which the angle lies. as the quadrant changes the sign of y changes and the sign of x remains the same. c. the statement does not make sense because the sign of the tangent function depends on the quadrant in which the angle lies. as the quadrant changes the signs of x and y change. d. the statement makes sense because the sign of the tangent function does not depend on the quadrant in which the angle lies.

Explanation:

The tangent function $\tan\theta=\frac{y}{x}$ in the coordinate - plane. The sign of $\tan\theta$ depends on the quadrant in which the angle $\theta$ lies. In the first quadrant $x>0,y > 0$, in the second quadrant $x<0,y>0$, in the third quadrant $x < 0,y<0$ and in the fourth quadrant $x>0,y < 0$. Just knowing $\tan\theta=\frac{4}{3}$ does not fix the signs of $x$ and $y$ as they can both be positive (first quadrant) or both be negative (third quadrant). So the signs of $x$ and $y$ change depending on the quadrant.

Answer:

C. The statement does not make sense because the sign of the tangent function depends on the quadrant in which the angle lies. As the quadrant changes the signs of x and y change.