The table below shows the reference angle, α , in quadrant I which corresponds to the angle, θ , in quadrants II, III, and IV.
Quadrant 
Angle θ 
Reference angle α 
Diagram 
II 
90˚ < θ < 180 ˚ 
α = 180 ˚ – θ 

III 
180˚ < θ < 270 ˚ 
α = θ – 180˚ 

IV 
270˚ < θ < 360 ˚ 
α = 360 ˚ – θ 
Determine the reference angle that corresponds to each of the following angle.
a) 165˚
b) 249˚
c) 328˚
a) 165˚ is in quadrant II (90˚ < 165˚ < 180˚ )
The reference angle is 180˚ – 165˚ = 15˚
b) 249˚ is in quadrant III (180˚ < 249˚ < 270˚ )
The reference angle is 249˚ – 180˚ = 69˚
c) 328˚ is in quadrant III (270˚ < 328˚ < 360˚ )
The reference angle is 360˚ – 328˚ = 32˚
What are reference angles are and how to find them, and then how to use them to determine the sine and cosine values of angles greater than ninety degrees?
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