Question

the terminal side lies in the third quadrant and is perpendicular to the line 3x + 5y = 0?

Answer 1

Answer on Question #63490 – Math – Analytic Geometry

Question

The terminal side lies in the third quadrant and is perpendicular to the line $3x + 5y = 0$?

Solution

The normal vector of the line $3x + 5y = 0$ is

$$\vec{n}_1(3,5).$$

Vector $\vec{n}_2(5, -3)$ is perpendicular to the vector $\vec{n}_1(3,5)$.

The equation of the terminal side:

$$5x - 3y = 0 \Rightarrow \frac{x}{3} = \frac{y}{5}$$

Angle:

$$\varphi = 180{}^\circ + \tan^{-1} \frac{5}{3} = 180{}^\circ + 59{}^\circ = 239{}^\circ.$$

Answer: $\varphi = 239{}^\circ$

www.AssignmentExpert.com