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The reference angle is the positive acute angle that the terminal side makes with the x-axis. The initial side of your angle is assumed to lie on the positive x-axis.
1) 50° (is in Q I, between 0° and 90°) has reference angle of 50°
2) 120° (is in QII, between 90° and 180°)has reference angle of 60°
(I subtracted 120 from 180.)
3) 6π/7 (is in Q II) has a reference angle of π/7
(I subtracted 6π/7 from π. Notice that
8π/7 (a Q III angle) would have the same reference angle.)
4) 3.3 (is presumed to be radian measure, a pure number without units, like #3; is in Q III) has a reference angle of 0.1584073464102067615373566167205.
(I subtracted your angle from π; then took the absolute value of the negative difference. Alternatively, you could just subtract π from your angle. You can round off to whatever accuracy you require.
5) 300° (is a Q IV angle) with a reference angle of 60° I subtracted 300 from 360.
6) -145° (is a Q III angle; the negative means that you rotate clockwise from the positive x-axis, instead of CCW) has a reference angle of 45° (I know that 145° be it positive or negative is 45° from 180°.)
Hope this helps.
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In general, positive angles are measured CCW from the positive x-axis. Negative angles are measured CW from the positive x-axis. With a perpendiular to the x-axis you generate 4 quadrants QI is upper-right;
QII is upper left; Qiii is lower left; Qiv is lower right (you count CCW). ±360° is a complete revolution as is ±2π.
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- Thank you so much for your help, I really appreciate it. I am not that smart in math and I am having a really hard time understanding a lot of what it being taught, so everything that you have provided has helped me greatly. Thank you again!!