Question

question 8 (1 point)
in which quadrants are the tangent ratios negative values?
a) third and fourth
b) first and second
c) second and third
d) second and fourth

Explanation:

Step1: Recall the formula for tangent

$tan\theta=\frac{y}{x}$ (where $(x,y)$ is a point on the terminal side of the angle $\theta$ in standard position).

Step2: Analyze the sign of $tan\theta$ in each quadrant

• First quadrant: $x>0$ and $y>0$, so $tan\theta=\frac{y}{x}>0$.
• Second quadrant: $x < 0$ and $y>0$, so $tan\theta=\frac{y}{x}<0$.
• Third quadrant: $x < 0$ and $y < 0$, so $tan\theta=\frac{y}{x}>0$.
• Fourth quadrant: $x>0$ and $y < 0$, so $tan\theta=\frac{y}{x}<0$.

Answer:

D. second and fourth