Question 1203785
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sin(θ) = 4/5
θ = arcsin(4/5) or θ = 180 - arcsin(4/5)
θ = 53.1301° or θ = 126.8699°
Both are approximate.


Arcsine refers to inverse sine, denoted on many calculators as the button *[tex \large \sin^{-1}]
Take note how sin(53.1301°) = 4/5 = 0.8 approximately and also sin(126.8699°) = 4/5 = 0.8 approximately as well.


The answer we want is either θ = 53.1301° or θ = 126.8699°


Which one do we pick? We go for the one that makes cosine negative.
cos(53.1301°) = 0.6 = 3/5
cos(126.8699°) = -0.6 = -3/5


Therefore, <font color=red>θ = 126.8699° approximately</font>


To convert to radians, multiply by the conversion factor pi/180.
This would mean:
126.8699° = 126.8699*(pi/180) = 2.2143 radians approximately
In my opinion, degrees are easier to work with in this context.


Side note: The angle 126.8699° is in quadrant 2, aka the northwest quadrant.
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