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

User Ryosuke Hujisawa
by
3.0k points

1 Answer

9 votes
9 votes

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).

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((|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((|-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).

User Barry Carlyon
by
3.4k points