Question

If the terminal side of an angle (θ) goes through the point (4 , -3) what is (θ)?

Answer 1

Answer:

The family of directions of the given vector is represented by $\theta = 323.130^{\circ} \pm 360\cdot i$, $\forall \,i\in \mathbb{N}_{O}$.

Step-by-step explanation:

According to the given information, vector stands in the 4th Quadrant ($x > 0$, $y < 0$) and direction of the vector ($\theta$) in sexagesimal degrees, is determined by following definition:

$\theta = 360^{\circ} - \tan^{-1} \left(\frac{|y|}{|x|} \right)\pm 360\cdot i$, $\forall \,i\in \mathbb{N}_{O}$

Please notice that angle represents a function with a periodicity of 360°.

If we know that $x = 4$ and $y = -3$, then the direction of the vector is:

$\theta = 360^{\circ}-\tan^{-1}\left(\frac{|-3|}{|4|} \right)\pm 360\cdot i$

$\theta = 323.130^{\circ} \pm 360\cdot i$

The family of directions of the given vector is represented by $\theta = 323.130^{\circ} \pm 360\cdot i$, $\forall \,i\in \mathbb{N}_{O}$.