Answer:
⇒ 60 degrees
⇒ 45 degrees.
⇒ 60 degrees.
⇒ 30 degrees.
Explanation:
The reference angle is the smallest angle between the terminal side and the x-axis.
[tex](1)\ \theta = 300^o[/tex]
300 degrees is in the 4th quadrant.
So, the reference angle is
[tex]\alpha = 360 - \theta[/tex]
[tex]\alpha = 360 - 300[/tex]
[tex]\alpha = 60^o[/tex]
Hence, the reference angle of 300 degrees is 60 degrees
[tex](2)\ \theta = 225^o[/tex]
225 degrees is in the 3rd quadrant.
So, the reference angle is
[tex]\alpha = \theta - 180[/tex]
[tex]\alpha = 225 - 180[/tex]
[tex]\alpha = 45^o[/tex]
Hence, the reference angle of 225 degrees is 45 degrees
[tex](3)\ \theta = 480^o[/tex]
480 degrees is in the 2nd quadrant (i.e. 480 - 360 = 120)
So, the reference angle is
[tex]\alpha = 180 - \theta[/tex]
[tex]\alpha = 180 - 120[/tex]
[tex]\alpha = 60^o[/tex]
Hence, the reference angle of 480 degrees is 60 degrees
[tex](2)\ \theta = -210^o[/tex]
-210 degrees is in the 2nd quadrant (i.e. 360 - 210 = 150)
So, the reference angle is
[tex]\alpha = 180 - \theta[/tex]
[tex]\alpha = 180 - 150[/tex]
[tex]\alpha = 30^o[/tex]
Hence, the reference angle of -210 degrees is 30 degrees
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