Unit Circle
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Unit Circle
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How to calculate the Unit Circle in Radians in detail?
I have the unit circle and I know what the basic angles are in Radians from the graph. My question is: WHAT ARE THE CALCULATIONS IN DETAIL to find that angle 120 is 2pi / 3. More specifically, how did he find the 2 and the 3 that appear in the solution? Likewise, where does the 3pi/4 come from? and the 5pi/6 and so on... I want to be able to hand calculate that when given an angle. Say the angle is 266, what is that in radians?
Use the relation
2π radians = 360° ( or π radians = 180°)
To put 120° into radians.
(120 / 360) X 2Ï€ radians
= (1/3) X 2Ï€
= 2Ï€/3 radians
Similarly 30 °
(30 / 360) X 2Ï€
= π/6 radians
60°
(60 / 360) X 2Ï€
= (1/6) X 2Ï€
= π/3 radians
45°
(45 / 360) X 2Ï€
= (1/8) X 2Ï€
= π/4 radians
266°
(266 / 360) X 2Ï€
= (0.74) X 2Ï€
= 1.48Ï€ radians ( or 1.48 X 3.14 = 4.65 radians)