## FINDING ANGLES IN OTHER QUADRANTS USING REFERENCE ANGLES

Finding Angles in Other Quadrants Using Reference Angles :

Here we are going to see, how to find the angles in other quadrants using reference angles.

Finding the Measure of the Reference Angle :

The reference angle is the acute angle formed between the terminal arm and the x-axis. The reference angle is always positive and measures between 0° and 90°.

## Finding Other Angles in Other Quadrant with Given Reference Angles

To determine the other angles in other quadrants using reference angles, we have to use the following table.

The reference angle always be lesser than 90 degree.

 Angles in quadrants2nd quadrant3rd quadrant4th quadrant Formula180 - given angle180 + given angle360 - given angle

Question 1 :

Copy and complete the table. Determine the measure of each angle in standard position given its reference angle and the quadrant in which the terminal arm lies. Solution :

(a)  72

Let θ be given angle.

Required angle in 4th quadrant  =  360 - θ

=  360 - 72  =  288

Hence the required angle is 288.

(b)  56

Let θ be given angle.

Required angle in 2nd quadrant  =  180 - θ

=  180 - 56  =  124

Hence the required angle is 124.

(c)  18

Let θ be given angle.

Required angle in 3rd quadrant  =  180 + θ

=  180 + 18  =  198

Hence the required angle is 198.

(d)  35

Let θ be given angle.

Required angle in 4th quadrant  =  360 - θ

=  360 - 35  =  325

Hence the required angle is 325. After having gone through the stuff given above, we hope that the students would have understood "Finding Angles in Other Quadrants Using Reference Angles".

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