trig find angle in each quadrant with common reference
I am looking back at a quiz I took a year ago and the question is as follows:
Find an angle in each quadrant with a common reference angle with 240 degrees from $0\le \theta\le 360^\circ$
The angle $240^\circ$ is in the third quadrant so...
I think the answer is
quadrant 3: 240 degrees bc 240 is in quad 3
quadrant 1: |180 - 240| = 60
quadrant 4: 360 - quad1 = 360-60 = 300
quadrant 2: not sure about itIs this the right idea and am I on the right track?
$\endgroup$2 Answers
$\begingroup$If the angle that all are related to is the reference angle for $240$, then that reference angle is $60$.
Now, with the reference angle of $60$, then it's going to be $60$ (Q1) then $180-60=120$ (Q2) then $180+60=240$ (Q3) and $360-60=300$ (Q4)
Reference angles are always acute angles and are always measured from the horizontal ($x$-) axis. You have found that $240^\circ$ has reference angle $60^\circ$. Therefore, four angles with the same measure, one in each quadrant are $0^\circ + 60^\circ = 60^\circ$, $180^\circ - 60^\circ = 120^\circ$, $180^\circ + 60^\circ = 240^\circ$, and $360^\circ - 60^\circ = 300^\circ$. Notice that in all four cases, we start with a quadrantal angle on the horizontal axis -- $0^\circ$, $180^\circ$, and $360^\circ$ -- then proceed into the quadrant by addition or subtraction of the reference angle, $60^\circ$.
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