Question #0c74b

1 Answer
Y
May 7, 2017

sin(9480^@)=sin(120^@)=sqrt(3)/2sin(9480∘)=sin(120∘)=√32

Explanation:

(I have assumed you have wrote the angle in degrees rather than radians although there isn't a degree symbol)
We can first start by simplifying the expression inside the sine function:
sin(90^@*105^@+30^@)=sin(9450^@+30^@)=sin(9480^@)sin(90∘⋅105∘+30∘)=sin(9450∘+30∘)=sin(9480∘)
Here we must find the reference angle of 9480^@9480∘:
Since 360^@360∘ is one full circle around the unit circle, we can do:
9480 mod 360 = 120 to find the remainder when 9480 is divided by 360.
Therefore sin(9480^@)=sin(120^@)=sqrt(3)/2

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