Question #0c74b

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Y
May 7, 2017

#sin(9480^@)=sin(120^@)=sqrt(3)/2#

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^@)#
Here we must find the reference angle of #9480^@#:
Since #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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