Math

QuestionDraw the angle 150150^{\circ}, find its reference angle, and identify the quadrant of its terminal side.

Studdy Solution

STEP 1

Assumptions1. The angle is given in degrees. . The angle is measured in standard position, which means the initial side of the angle is on the positive x-axis.
3. The reference angle is the acute angle formed by the terminal side of the angle and the x-axis.
4. The quadrants are numbered counterclockwise, with Quadrant I in the upper right and Quadrant IV in the lower right.

STEP 2

First, we draw the angle in standard position. The angle is 150150^{\circ}, which is more than 9090^{\circ} but less than 180180^{\circ}. This means the terminal side of the angle lies in the second quadrant.

STEP 3

The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. In the second quadrant, the reference angle can be found by subtracting the given angle from 180180^{\circ}.
Referenceangle=180GivenangleReference\, angle =180^{\circ} - Given\, angle

STEP 4

Now, plug in the given angle to calculate the reference angle.
Referenceangle=180150Reference\, angle =180^{\circ} -150^{\circ}

STEP 5

Calculate the reference angle.
Referenceangle=180150=30Reference\, angle =180^{\circ} -150^{\circ} =30^{\circ}The reference angle is 3030^{\circ}.

STEP 6

Since the terminal side of the angle lies in the second quadrant, we can state that the angle is in Quadrant II.
The angle 150150^{\circ} in standard position has a reference angle of 3030^{\circ} and lies in Quadrant II.

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