Solve sinx - radical 3 cosx = 1 for all values of x

Calculus
Tutor: None Selected Time limit: 1 Day

Please show all work. Thank you!

Jan 28th, 2015

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.



Jan 28th, 2015

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