Question

Determine the quadrant in which the terminal side of the given angle lies.

1,165


I

II

IIII

IV

Answer 1

quadrant III

Explanation:

first we need to reduce the angle 1165°

1165 - 180 - 180 - 180 - 180 - 180 = 265°

since our reduced angle is 265°, this means that its in between the angles 180 ° and 270° which is in the third quadrant.

When you encounter another problem like this, just subtract it to 180° until it reaches an angle that is greater than or equal to 360°. Hope this helps! ;)

Answer 2

A. I

Explanation:

The sum of the angles in the four quadrants equals
`360^(o)`.

Given an angle
`1165^(o)`, then;

`(1165)/(360)` = 3.236111....

So that,

`360^(o)` x 3 =
`1080^(o)`

Thus,

`1165^(o)` -
`1080^(o)` =
`85^(o)`

We have;

`0^(o)` <
`85^(o)` <
`90^(o)`

Therefore, the terminal side would lie in the first quadrant. The correct option is A.