Question #1d7ab

1 Answer
Bdub
Jun 14, 2017

#S={pi/6,(5pi)/6}#

Explanation:

Note that this equation looks like a quadratic equation but instead of x we have sin x and a=4, b= -4, and c= 1, so we will use the quadratic formula to solve. That is,

#x=(-b+-sqrt(b^2-4ac))/(2a)#. Therefore,

#sinx =(4+- sqrt(16-4(4)(1)))/(2*4)#

#=(4+-sqrt(16-16))/8#

#=4/8#

#sin x = 1/2#

#x=sin^-1(1/2)#

#x=pi/6 + 2pin or x=(5pi)/6+2pin#

Put in #n=0# we have #x=pi/6 or x= (5pi)/6#

Note that if we put in any other n value the answers will fall outside of the restriction # [0,2pi)#. Hence, our solution set is

#S={pi/6,(5pi)/6}#

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