Description
Please show all work. Thank you!
Explanation & Answer
Sinx - radical3 Cosx = 1
Divide thru' out Radical {of 1 squared + (rad3)squared} = Radical (1 + 3 ) = 2
1/2 sinx - (rad3)/2 Cosx =1/2 Use trig ratios of standard angles and it is easy to guess that 1/2 = Cos 60deg and rad3/2 = Sin 60deg.So our equation is now
Cos60Sinx -Sin60Cosx = 1/2 this can be written as Sin(x-60) = 1/2.
One solution to the above equation will be 30deg.(In radian form,60deg = Pi/3 and 30deg is Pi/6)
So the General solution of the given equation is
x-pi/3=nPi + (-1)^nPi/6 or x = nPi + (-1)^nPi/6 + Pi/3 for all values of n belonging to Z,the set of integers.
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