Question

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

Answer 1

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)`.