QuestionDraw the angle $-240^{\circ}$ in standard position and identify its quadrant.

Studdy Solution

STEP 1

Assumptions1. The angle is given in degrees. . The angle is measured in standard position, which means the initial side is on the positive x-axis.
3. The angle is negative, which means it is measured clockwise from the initial side.
4. The four quadrants are numbered I to IV, starting from the positive x-axis and moving counterclockwise.

STEP 2

First, we need to understand what the given angle means. A negative angle is measured clockwise from the positive x-axis.
$-240^{\circ}$

STEP 3

We know that a full rotation around the circle is $360^{\circ}$ . So, we can add $360^{\circ}$ to the given angle to find its positive equivalent.
$Positive\, equivalent = -240^{\circ} +360^{\circ}$

STEP 4

Calculate the positive equivalent of the given angle.
$Positive\, equivalent = -240^{\circ} +360^{\circ} =120^{\circ}$

STEP 5

Now that we have the positive equivalent of the given angle, we can determine the quadrant in which the terminal side of the angle lies.1. If the angle is between $0^{\circ}$ and $90^{\circ}$ , it lies in Quadrant I.
2. If the angle is between $90^{\circ}$ and $180^{\circ}$ , it lies in Quadrant II.
3. If the angle is between $180^{\circ}$ and $270^{\circ}$ , it lies in Quadrant III.
4. If the angle is between $270^{\circ}$ and $360^{\circ}$ , it lies in Quadrant IV.

STEP 6

By looking at the calculated positive equivalent of the given angle, we can see that $120^{\circ}$ lies between $90^{\circ}$ and $180^{\circ}$ . Therefore, the terminal side of the angle lies in Quadrant II.
The terminal side of the angle $-240^{\circ}$ lies in Quadrant II.

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