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°.
To determine the other angles in other quadrants using reference angles and the following table.
The reference angle always be lesser than 90 degree.
Angles in quadrants 2nd quadrant 3rd quadrant 4th quadrant |
Formula 180 - given angle 180 + given angle 360 - given angle |
Question :
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.
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